I have been researching that question myself. In my state, heat detectors are not classified as 'life safety devices'. They are 'property protection devices'. They can be combined with smoke detectors when used in limited areas such as a restaurant kitchen. Of course, there is no specific code on haunted houses, so I am waiting for a ruling from my fire marshal.
The principle drawback to the heat detectors are that they are not available (that I have been able to locate) in a version that can simply be interconnected by a single wire like smoke detectors. They are only usable as part of a complete panel system. In my state, and I assume most others, smoke detectors must be interconnected in such a fashion that if one goes off they all do.