How do i fix rav4 2002 refuse to start when hot but very ok when engine is cold

no engine size told.
well there are like vast causes of this
my engine starts but stalls.
even parked in a drive way , transmission in pARK?
The macro causes are 3. (100 yeas same gas/petrol) rules
bad spark
bad fueling (even bad fuel)
bad engine (cam belt slipped) this fail trumps above.
a tech tests them all in order.(based on age, and miles) saves time.
no miles on car stated 100k 200k, 300k miles or more?
when was the last tune up (filters all, spark and belts)
not told. and matters huge.
does it fail cold and hot engine both, or can never get it hot
hot = means normal engine temp, 180f to 200f
is RPM started up, cold 1500RPM or less (or happens too fast to tell)
does engine die just as you shift to DRIVE.?
failures parked are the most easy to find, (moving fast failures hard)
tell more and get more, tell all things the engine does, in all modes of use. AND WHEN AND HOW LONG IT TOOK TO FAIL.
or hot engines turned off will not staRT (BUT CRANKS FAST)?
THERE IS A STORY HERE BEGGING TO COME OUT BUT DID NOT.

THE MICRO LIST IF CAUSES ARE HUGE.
EVEN a bad wire vast.

how soon after it starts does it stall,
1second 1 hour ? what, ?
some engines fail hot soaked, starts cold, but never hot

WHY NOT GET A SHOP TO FIX IT. IN USA AN ASE SHOP !

Start with a new coil and plug wires, along with plugs.

First you should make sure you have sufficient coolant and fresh oil. If engine is over heating, metal parts will swell. Is it turning over ok and not starting? Or is having trouble cranking/sounding like the battery is weak? Explain symptoms.

check for a bad fuel pump relay. One of the first signs of a failing DME/Fuel Pump is difficult hot starting. Quite often when the DME/Fuel Pump relay starts failing the car will start without problems when it is cold. However, when the car has been operated at normal operating temperature for a while, it will refuse to start. Its worth a try! (usually 30 minutes to 1 hour), the car will again start without problem. Is this the case! Good-Day!

The PCM (power control Unit) controls the idle speed base in input from various sensors, one of them it's the coolant temp sensor, this sensor may be telling the computer that the engine it''s too cold and the computer will keep the idle up to help the engine warm up faster

Is cranking speed slow? Do a voltage drop test on battery cables.and a high output amp meter to test starter draw. normal ampere draw should be 250-350 amps cold and 300-375 amps hot as engine turns these readings should drop to 200-250 amps if not bad starter.

intermittent are hard to find.
as they say" if it ain't broke, you can't fix it" applies
but in truth, we lay in traps to find this.
this is true with all machines, not just sx4
facts: (random no starts) but always cranks fast.
only fails cold engine. never hot. (does restarts hot work?)
seems yes.
seems you have full 12vdc power at all times.
seems the engine is ok. as it is not heat rlelated or the classic hot soak fails.
so what is it.
well, its 1 of these.
1: lost spark, simple tests, do so when failed.
2: bad fueling. (too much or too little)
the tests for each failure are dead simple and work on any engine.
ask.

I have the same problem with my F150 4.6. Long cranking when out door tempurature is hot. Engine temp gauge indicates normal engine tempurature. Looking for solution.

The starter operates great when cold. When the engine gets to its normal operrating tempreture the starter gets hot. An old starter will have an expanded armature from this causing the starter to drag or just freeze up hot . When its cool it will start again. This will eventuly get hot and the armature will go bad forever on you so get it changed soon

Might be an oil issue. Oil when hot might be too thick for the pump to pump the oil easily in the engine. Check that and if not that come back.