You have got to be a little more specific when talking about the no start condition.
When it is at temp and does want to start, is the engine cranking?Or is the engine cranking but just not starting?

Different type of no start deals with different circuits.

Note: Did you clean the ignition wire going to the starter solenoid?
And did you clean the terminal from battery to starter post?

It attempts to crank over like a very weak battery. If I keep turning key to off and try again, it does the same thing. Crank maybe twice then nothing. Again, if I just leave it alone for a while 30-60 minutes and it cools down, it starts right up like there is nothing wrong. Does that explain it better?

Maybe you could try this addl test, You will need someone to observe the results.

With the headlights on, attempt to start the vehicle when hot and normally won't start.
Watch the headlights and see what they do.
Do they go dim, if so battery questionable, cable connection questionable, starter internal problem.
If the lights don't go dim, problem is in starter circuit and .or starter.

I know you stated it has a new starter.
That could mean a brand new one and you keep the old starter
I could also mean you bought a rebuilt exchange starter where they exchanged your starter for a rebuilt one.

When we put 3 starters on a vehicle and still have the same problem , guess what, IT ain't the starter !!!
Of course if you are getting cheap rebuilt starters , unfortunately , you could be getting what you paid for.

If you carefully pour the cold water on specific parts/areas and the vehicle finally starts, concentrate your efforts to that area.
Between what "A Visitor" suggested and the above checks you should be able to pin down the cause.

So, cold it starts up every time.
When hot, it cranks a little. Once or twice then nothing. Like a weak or dead battery.

Sounds like a bad starter. But, having already changed two starters ...
Must do a few more tests.
Is it an accessory pulley that is stuck?
Is the engine hydro locked due to open injectors?
Try swapping the starter relay in the fuse box?
Still need to clean cable terminal at the starter to eliminate that as a cause of this issue.

Well, good luck

Thanks avistor and hanky. I will try these suggestions soon. Life has been busy lately, but hope to be able to try these additional suggestions in the next few weeks and let you know if problem still exists. Also, to clarify the current starter is brand new, not a rebuilt.