On our cars, the solenoid's function is to act as a high-amperage switch for the starter motor, and to kick the drive gear into the flywheel teeth.

Does the drive gear mesh with the teeth? No? Solenoid or starter shims.
Does the starter try to turn the engine? No? Solenoid or bad starter.
Does the starter engage properly but turn the engine too slowly? Yes? Starter.

The cars that were built with long branch manifolds 40 years ago did not have hot start issues...if they did there would have been many complaints. Instead, there were different starters offered, the heavy duty starter and solenoid on the higher powered models. This is like the best rebuilt starters, not like the typical discount auto "rebuilt".

http://www.procarcare.com/icarumba/resou...a_starting1.asp

http://www.indiacar.com/infobank/battery1_od.htm

And the cure:
http://www.alcester-racing-sevens.com/starter_maintenance.htm

If your starter is already degraded from heat, repair it first.

The last article also describes a relay modification. Our cars do not incorporate a starter relay. Converting the long current-carrying ignition circuit to a simple trigger switch by using a relay mounted relatively close to the starter could alleviate the remaining issues. And unlike a remote starter solenoid, this modification can effectively shorten the starter primary circuit and leaves the secondary circuit unaltered.