Can't really decide on who's the culprit (Tamaki's the fishiest, but too obvious), but I think the motive is the culprit:
1. believing that Takehiko was actually murdered,
2. discovering the method used to burn him to death while making it totally look like an act of God,
3. suspecting that the murderer is one of them, and
4. using that method in the present to gauge who Takehiko's murderer was.
You know, after seeing fire sprouting on someone out of nowhere not once, but twice very recently, I wouldn't wanna be alone, especially if I have to drive.