[Mr Jody]

I don’t think heat cycling would give you the single loud snap that you are hearing. This is usually a series of smaller, less intense snaps.

I may not be telling you anything you haven’t already thought of, but just in case, since so far nothing indicated it is engine related. Since it seems to be related to stopping or low speeds, to check out the possible causes, try to find somewhere where there is a slight decline and with no traffic like a parking lot or quiet side street where you can turn the car off and let it coast. Then apply the brakes. Maybe try it several times at different intensities, with and without depressing the clutch, and moving the gearshift lever if you were moving it as you were making stops when you heard the noise before. Also try a few tugs on the parking brake if nothing else yields any sound. With the car not running, you may be able to hear similar but less intense sounds that would otherwise be masked by the engine noise.

You could also get it up on jack stands so you can get under it to look for moving parts and listen while an assistant performs actions similar to those above. And of course check for anything loose while you are under there, and to see if there is any contact between any moving parts and the body and frame. Check motor mounts and the transmission support, shift linkage. and shocks and their springs and mounts as well. The only downside to this is the suspension geometry is changed when it is on jack stands, so if there is somewhere you can take it where you can get under it with the weight still on the tires would be good. While on the stands, you could also manually rotate each tire to listen for sounds, with and without the above actions, or even crank the car and let the drive train run at low speeds. I wouldn't operate it at higher speeds while on the stands if the u-joints appear to be overly angled from the norm.

Like I said, maybe nothing you haven’t already thought of, just trying to help in recreating the scene, or sound, of the crime.