Hudson,
I understand that this delay between overheat and fire warning is a feature olf old 737-300 simulators. In later version simulators the actuation of the fire warning on the instructor panel causes simultaneous overheat indication and fire warning.
The old 737 simulators, and many other old (and some new) simulators still do the same thing. What the simulator programmer has tried to do is to replicate the real world situation. Consider the fire, temperature is rising, not in a microsecond, but over 5 to 6 seconds - real life. The Overheat warning, with a lower temperature threshold will trip first, and, as temperature rises further, trips the fire warning at it's much higher threshold.
This has always been the simulator instructor's problem, timing of an event -
I want it, and I want it now! You want to give the student a fire just before V1, for example, and the damned thing goes off after Vr.
In several simulator calibrations / acceptances that I was involved with, we managed to cajole the manufacturer's technicians into 'instantifying' (is that a word) various scenarios such as this, so that the instructor could introduce the fault at the appropriately timed moment.
A check of the "Fault Description" should reveal the programmer's intention, maybe your own sim techs can 'engineer' a bit of deception.
I well remember that loss of oil pressure was one such problem, the programme reasonably caused the oil to leak away, quantity steadily dropped, temperature slowly rose, and finally, 2 to 3 minutes after takeoff (when you wanted it before V1) the oil pressure finally failed.
Sometimes.....Ya gotta cheat a bit.