fuel pump?
Possibly, you have a broken timing belt.
It would die and not restart. Yes it may restart! I have had modules quit when they get hot and work again when they cooled down.
it could be of running it with out oil.
Yes! I got a 1994 MX6 and it would shut down while driving when your oil is low.
That happened to my 1996 F-150. Ended up being my oxygen sensor. It would crank, but not start.
had same problem with my probe stalling whilst driving after stopping short spell and would then restart. answer was located in immobilizer circuit which cut in at wrong times only cure was to have immobilizer disconnected.
doubt that a t-stat would cause a car to shut down and restart when cold check for an ignition module proublem
ClickStartShut Down ComputerPress "restart"
clogged fuel filter
One posibility to check would be the timing belt. If it broke while driving your car will stall and will not start again. If it was the timing belt you may have a more costly repair bill then just the belt.
the main brain box.