Did Khalid ibn al-Walid cut off the head of Malik ibn Nuwayrah and cook over it?

Some historians mentioned this story, but its authenticity has not been proven. Furthermore, regarding Khalid's killing of Ibn Nuwayrah, some mentioned that he misinterpreted [the command] and erred, and Abu Bakr excused him. Others mentioned that the prisoners were in a cold place, so Khalid said, "Warm your captives," and some understood that he meant for them to be killed, so they killed them. Many biographers mentioned that Khalid did not personally kill Ibn Nuwayrah, but rather Dhirar ibn al-Azwar killed him.