Hi, welcome to JA.
It may very well be the starter motor, however this starting circuit incorporates an Inhibitor Relay and Inhibitor Switch. The relay is found in the relay box at the driver front of the van, under the hood. In the top row you should see 6 spots for relays, it is the 3rd relay from the left. I would replace the relay first and see if this cures the problem. The correct step to take would be to use a multimeter to test for good voltage to the starter terminals when this problem is occurring, if this testing cannot be done, the next best step to take would be to replace this relay since it interrupts the starter signal during starting. Also, if there is an after market alarm system installed it may be interfering with the starter signal as well, as I have seen in many cases. If there is an after market system installed, it would be best to have voltages to the starter signal tested before replacing any component.
In my experience, starter motors which fail after the engine is warm, tend to operate again within a short period of cooling...rarely overnight as explained in your condition. If you have a multimeter handy, let me know if you'd like testing procedures.
Sure thing. Take your multimeter and place it on DC volts scale. WHEN THE ENGINE IS NOT CRANKING, you will place the positive lead on the red wire with the white trace on it at the starter. The wire will need to be connected to the starter terminal so try to get your meter lead on the post itself or through the back of the connector. Have an assistant turn the ignition key to the crank position. You should see around 12 volts there if the engine is not cranking. If there IS voltage there, the problem lies in the starter itself, but be sure you also have a good 12v or so on the large white lead from the battery on the starter as well. Also, during this testing, be sure your meter black (ground) lead is grounded to the battery negative or good engine ground. If you have good voltage at the starter on both terminals, and the engine is not cranking, you have a problem internal to the starter. However, if the red/white wire has no voltage or low voltage, you will test next at the inhibitor relay terminals. Do this by accessing the wiring loom underneath the relay box at the driver front of the engine compartment. The wire colors for the inhibitor relay are Light green/Black, Dark Red, Blue/White, Green/White, and the Red/White. Probe the Red wire with your meter positive lead and the black lead grounded. Have an assistant turn the ignition to the crank/start position. You should see 12 volts on the Red wire. If you see good voltage here the ignition switch is operating correctly. Than probe the Red/White wire at the relay. If no voltage here in the crank position, you either have a bad relay or a bad Inhibitor Switch on the transmission which is not powering the relay. To further elliminate a bad Inhibitor Switch probe the Light Green/Black wire at the relay with the ignition key ON, you should see 12 volts here. If you have a good 12 volts on the Light Green/Black wire with the key on and good voltage on the Red wire with the key in cranking position, but no voltage on the Red/White wire to the starter - replace the Inhibitor Relay.
Let me know if yoiu run into any trouble with this.
If you have good voltage at the starter on both terminals, than the starter should be replaced. Good voltage on both terminals would mean that the inhibitor switch and relay are doing there job and supplying the signal to the starter, as well as the ignition switch. I wouldn't replace the starter without testing voltages, there is a possibility the inhibitor switch or the ignition switch could be at fault as well if the relay is not the cause. If you can't complete the testing, replace the relay and see if the problem persists. If it does, try starting it in neutral rather than park...if it starts in neutral when this problem is occuring, it can indicate a faulty inhibitor switch on the transmission. You can also opt to remove the starter and take it to a local auto parts store that can bench test it under a load...but do this after driving for awhile and get the starter hot so it can be better bench tested for this problem. Again, in my experience it is usually an Inhibitor Relay when the starter isn't cranking after the vehicle is warm. And in the cases where it is the starter, I've only had to let the enging cool down for an hour or two, but never overnight.
Thank you so much for your valuable time sir.
May God Bless,