Symptoms like that are very often a faulty starter, but I noticed you said the starter is new, so........I dunno. What brand of starter? You could have purchased a starter which was weak/faulty/cheap even though it was new.

 

Try doing this. Spray starting fluid into the throttle body when engine is warm. Also verify spark is getting to the plugs when the engine is warm.

 

Something in your starting system is affected by heat. Happens occasionally. I presume other things still have power correct? I would suspect something with a coil and you have replaced the starter already so how about the starter relay? I have personally experienced this intermittent issue on a dishwasher coil

 

For me, it sounds like an electrical issue with the ignition. I know it sounds far fetched, but just mimics this behavior. I’ve had a bent key before and the starter wouldn’t engage.

 

Are you certain there is no clicking? Torontoguy222 mentions the starter relay. When you turn the key to START, the starter should click and then send power to the starter solenoid (on the starter). The solenoid should make a much louder click (clunk!) and engage the starter. Normally you won't hear these as the starter will start to crank.

 

When my starter relay (the one under the driver's dash) went bad, it wasn't intermittent depending on the engine being warm/hot or not. I suppose a test for the relay (without having to remove the relay) would be when the engine is hot and the starter is not engaging to apply battery voltage directly to the starter (the skinny single wire I believe). If it starts when it otherwise would not (engine hot) then it is most probably the starter relay which is faulty. There is a test on the relay you can do with a multimeter (after removing the relay). Sorry, but I no longer remember what the numbers are for that. When I tested my relay, it was not within spec.

 

You can verify voltage from the starter solenoid to the positive battery terminal. The light blue wire should have 12v key on, engine off.

Locate the starter relay and apply voltage to the load side of the socket to verify the starter turns. What brand starter did you buy op?

 

If it cannot even crank then replace the starter. This is a no brainer.

 

Not necessarily. There are other components in the starting system you know!

 

Place volt meter at the terminals of the starter. Turn key and see if there is any voltage. If no voltage, other things are at fault. But if there is voltage, it must be a bad starter.

 

The neg of the voltmeter has to go to a suitable ground and the positive of the meter has to got to the starter SOLENOID (the small wire)...........................it will work the other way also but just saying