Starting problem

Hello: had a problem like this on a new chevy truck once. Turned out to be the starter. What happened is the crimps on the wires were poor and heat caused them to become poor connections until cooled off. I removed the starter, tore it apart, soldered all wire crimps within the starter and problem gone forever, but this requires some work and you have to know what you are looking for. You could just replace the starter. Another possibility that I have seen is exactly the same with the crimps, but was battery cables. I have seen a bad battery cable do the same thing. Problem with automotive electrical and most other electrical is the terminals placed on the end of the cable or wire. They are placed on the end of the wire and smashed (crimped) onto the wire. This may work when first done, but as time goes by these crimps become poor connections and cause your greif. The only way to properly install a terminal on the end of a wire is to crimp and then SOLDER the terminal to the wire, that makes the problems go away forever.
Good luck
Darryl.