A bad timing belt could make the engine shut down but it would only happen once, not sometimes.
could be the timing belt
bad ignition timing.
yes this will cause engine to run hot
Incorrect Timing Can Cause Backfire.
timing belt snapped
Happened to me in a Ford, I guess it could be many things but mine stoped because the Timing Chain broke
Sometimes the Timing belt tensioner will cause a tap or click until the engine is warm.
wrong timing can cause any engine to over heat. in fact if the timing is off it can cause hundreds of dollars of damage.
check your timing belt
The engine will turn on the starter, or with a wrench on the end of the crankshaft. However it will not run. If the Timing belt breaks, when the engine is running, this can cause extensive damage to the engine.
A timing chain, that needs to be replaced, can cause your engine to run rough and lose power. A broken timing chain can cause significant engine damage.
Your car has the 1NZ-FE engine featuring VVT-i (variable valve timing with intelligence). This is a non-interference engine, with a timing chain. While a broken chain could cause damage to your engine, it is less likely to cause damage on a non-interference engine, and if the chain is damaged (but not completely snapped) you will often know it because it will make a lot of noise (stop driving it at that point and get the chain replaced). The chain is generally considered good for 250,000 miles unless it begins making noise.