On February 4, 2015, the Egyptian news website Akhbarak.net reported that the Qatari Fatwa Center, a body belonging to the Qatari government, had removed from its website a fatwa permitting execution by burning. The Fatwa Center is part of Qatar's Religious Da'wa and Guidance Authority, which belongs to this country's ministry of religious endowments and Islamic affairs. According to Akhbarak, the Fatwa Center removed the fatwa from its website, Islamweb.net, a few hours after the burning of the Jordanian pilot, Mu'adh Al-Kasasbeh, by the Islamic State (ISIS) became known. However, a search of this site reveals that the fatwa, issued in June 2009, is still available on another part of the Qatari website, as well as two earlier fatwas that make a similar point.
The June 2009 fatwa was issued in response to a query by a reader who asked whether it was permissible to execute a Muslim by burning, adding that someone had told him about such cases. The fatwa issued in reply stated that, as a rule, the shari'a forbids burning people alive, but that some scholars were inclined to permit this as part of the principle of "measure for measure." This fatwa is similar in its content and conclusion to the fatwa issued by ISIS in the Syrian city of Raqqa to justify the burning of the Jordanian pilot, though ISIS's fatwa was issued in response to a question about the burning of infidels, not Muslims.  ISIS's fatwa stated that the burning of the pilot was justified because he had carried out airstrikes on Muslims, thereby causing them to be burned alive.
The following are excerpts from the three fatwas on the Qatari website.
The June 2009 fatwa on the Islamweb site
Some Religious Scholars Were Inclined To Permit This
"Question: Is it permissible to punish a Muslim, Sunni or Shi'ite, by burning him? Please inform me, because I received an email about a Muslim being burned, and I answered the person who sent me the email [with a quote from the hadith]: 'only the God of fire may punish with fire.' But he opposed my position to the point that I started to doubt its correctness.'
"Answer: According to the shari'a, punishment by fire is forbidden, regardless of a person's status, for it is written in the hadith: 'only the God of fire may punish with fire'... [So] this deed is a sin that is forbidden because of the injustice it involves. As for a punishment imposed by the Muslim leader on criminals, it is better for one who is deserving of death to be punished with an appropriate death, according to the hadith that says, 'if you must kill, then kill in the best manner'...
"[However,] some scholars advocated killing [a murderer] in the same way he killed [his victim], as written in the book Mukhtasar Khalil [by 14th century scholar Khalil ibn Ishaq Al-Maliki]: 'He must be put to death in the way he killed, even by fire.' In the Al-Sahihain collection of hadiths [it is said] that the Messenger of Allah 'crushed the skull of a Jew with two stones, just as [that Jew] did to the slave girl he killed.'"
Caliph Abu Bakr Punished A Man With Fire
At the end of the fatwa, links to two other fatwas are provided. One of them, titled "The Burning of Iyas bin 'Abd Yalil by the Righteous [Caliph] Abu Bakr," was issued in February 2006 in response to the following question: "How can we reconcile the Prophet's ban on burning with fire with [Caliph] Abu Bakr's burning of Iyas bin 'Abd Yalil during the Ridda Wars?..."
The fatwa issued in reply stated: "The Prophet's ban is valid. According to the honorable hadith, the Prophet said: 'only the God of fire may punish with fire'... [However], religious scholars were divided on whether this ban is absolute, or is only meant to [instill] humility [towards God]. [Shafi'i jurisprudent] Ibn Hajar [Al-'Asqalani] said in his book Fath Al-Bari: "This ban is not meant to prohibit [burning], but only to [instill] humility. The actions of the Prophet's Companions indicate that burning is permissible. The Prophet blinded members of the 'Uraina tribe with a hot iron. [Caliph] Abu Bakr punished criminals by burning in the presence of the Prophet's Companions, and [the Prophet's Companion] Khalid Ibn Al-Walid [also] burned people from among the apostates. Most of the scholars of Medina permitted to burn horses and chariots with the people inside... [Conversely, the scholar] Ibn Al-Munir and others said: 'There is no evidence [to support the view] of those who say it is permissible. The [punishment] of the 'Uraina tribesmen was in retaliation [for their deeds], or else was abolished [as a form of punishment]. Moreover, [we see that] a permit by one Companion of the Prophet contradicts a ban by another Companion. The case of the horses and chariots is a matter of necessity; that is, [such an act] is permissible if it is the way to overcome the enemy.'
"The story about Abu Bakr's burning of the believer Iyas bin 'Abd Yalil is recounted in the books of biography and history. [It is said:] 'Iyas bin 'Abd Yalil came to Abu Bakr and said to him: Give me weapons so I can fight the apostates. [Abu Bakr] supplied him with weapons and appointed him commander, but [Iyas] turned against the Muslims... Abu Bakr discovered this, and sent people to arrest [Iyas] and fetch him. Abu Bakr ordered to light a fire in the Medina mosque, and then he pitched [Iyas] into it, swaddled in cloths.'
"Thus, the scholars were divided with regard to the ban on burning by fire, as we have clarified, and those of them who said that this was forbidden made exceptions for cases in which this was permitted. There is no doubt that Iyas bin 'Abd Yalil's deed justified his burning. May Allah maximize the reward of the Caliph of the Messenger of Allah for his zeal for Islam."
Islam Permits Punishment Measure For Measure
The third fatwa, titled "The Limits of the Principle of Measure for Measure" and issued March 5, 2009, responds to a reader who asked how one could determine when to apply the rule of measure for measure against the enemies of the Muslims, and when not to apply it. The fatwa states:
"The correct principle of Islam is that there is permission to punish measure for measure, as long as this is does not violate our religion... The Koran commentators said that whoever is harmed by an unjust deed will have vengeance against the one who transgressed against him, if he succeeds in overcoming him, in a way that is similar to the injustice done to him, and he must not deviate from this to other deeds. In light of this, it is possible to kill a murderer as vengeance in the way that he killed... and for this reason, the Maliki [scholar] Khalil said in his book Mukhtasar [Khalil], 'He will be killed as he killed, even by fire, but not by means of intoxication or by means of sodomy'..."
The author of the fatwa stressed, "But if the aggressor kills in a way that is forbidden by shari'a, he must not be killed in a way that Allah has forbidden... The ratio of measure for measure is permitted as long as it [does not involve an act] forbidden by our religion."
 A link to this website is also found on the Qatari government portal, which invites readers to "contact Islamweb, which belongs to the Ministry of Religious Endowments and Islamic Affairs in the State of Qatar, for a shari'a opinion on any topic of interest."
 In 2008 there were reports that the Islamic State of Iraq (the previous incarnation of ISIS) had burned Iraqi tribesmen it had taken captive. Perhaps these were the incidents of which the asker had heard.
 See MEMRI JTTM report, "ISIS Issues Fatwa To Justify Burning Of Jordanian Pilot," February 4, 2015.
 Islamweb.net, June 17, 2009.
 This means to say that there are other stories about the Prophet's companions that indicate burning is forbidden, and therefore the stories about Abu Bakr and Khalid Ibn Al-Walid cannot be taken as conclusive evidence for the permissibility of burning.
 Islamweb.net, February 7, 2009.
 Islamweb.net, March 5, 2009.