@Sandwich I can't tell you why people are downvoting 'cause I didn't (and because I am not in a hive mind with them) but I can tell you why I have hesitated to upvote
Your answer contains much truth inside it, but the practical help of what to do is limited to the last paragraph, where it is also intermingled with condemnation: talk to them, and separately tell them you will have a hard time trusting them.
We are a group of five who rotates DMing with each quest. We have one DM who only does what he wants when he's DM, with no regard for other players, other DMs, or the rules, which forces the next DM in the rotation to scramble to salvage what is left from his quest. This one DM's quests consisten...
Greases tend to burn in a rather ugly, smoky, not very handy for arsonists way...
although part of that depends on your def. of "grease" -- animal fats burn more readily than saponified greases do
and even with a coating of grease on its surface, a 12" log will charbroil black and not present much if any opportunity for further heat penetration well before it fails
@Miniman Yeah, that answer hit my DANGER button quick, and then I realised it was perfectly fine. I tweaked it to not apologise or meta-mention commenting, since it was already doing a good job of referencing other answers while answering independently.
@Sandwich -- yes, Prestidigitation is handy -- my question is "can you get the interior of the log hot enough to smolder to failure with the limited ability of oxygen to penetrate the char layer?"
@SevenSidedDie Tbh, I think it's one of the best suggestions there, since it might allow the problem DM to have more fun as well as everybody else. And it doesn't involve splitting the group.