Car acts dead after it gets hot...

You guys are way too eager to throw money at stuff. Learn to troubleshoot. Learn to check stuff so you KNOW what is the matter

Possilbles:

FIRST start by "wiggle testing" and makiing sure starter connections are tight, as well as connections at relay and battery

The "circuit path" to fire up the starter between the ignition switch and starter relay

I am starting with the switch because you say the headlights work. The headlights get power at a splice in the black ammeter wire and so does the ignition switch. This means the switch and headlights both should have power, unless the splice failed which can happen but is rare

I am stopping at the output of the starter relay because you say you "jumped" it which means the wire going from the starter relay to the starter solenoid is good. By the way THOSE wires can fail, as the engine moves and vibrates "down there" and can break the connection in the wire

So the path is ignition switch--------through the start contacts---out the switch---through the switch connector (normally yellow wire)-- through the bulkhead connector---------to one of the flag terminals on the starter relay----through the relay coil------out on the remaining flag terminal---------to the neutral safety switch wire--------down to the transmission-----------to the neutral safety switch connector-----------to the neutral safety switch------------and to ground when in park or neutral

Read that all carefully each point noted is a POSSIBLE TROUBLE. Each terminal, each connector You could buy a new relay, a new ignition switch, and a new neutral safety switch and go to the work of putting them in the car only to find out that a poor connection was the culprit.

Get a test light, a meter, and a couple/ three "aligator clip" jumper leads and learn how to troubleshoot

1........Making certain the car is in park, look at the relay and pull the flag connector that is NOT yellow. Clip that relay terminal to ground, and try to crank the engine USING THE KEY. If it cranks, the problem is in the NSS switch, wireing, OR THE SHIFTER needs adjustment

2.....If the above does not crank the car, leave the terminal grounded above. Take a screwdriver/ jumper llead. Remove the second flag terminal (yellow). Now jumper power to the now exposed terminal, making sure the first is still grounded. Does it crank? No? Replace the relay. Does it crank? Yes? Trouble is in yellow start wire, bulkhead connector, ignition switch connector, or ignition switch

3....Assuming jumpering relay in (2) cranked engine, hook everything up "normal." Now go inside, access ignition switch (unbolt it from panel) and get it down where you can access it. Disconnect battery ground while doing that. When you have it down, "safe" and accessible, reconnect battery

Now acces the "S" connection (yellow) on ignition switch and back probe the terminal with a meter or test light. Twist key to start. Do you have voltage? Yes? Does the engine crank? No? then trouble is likely is bulkhead connector terminal. If it does NOT show voltage, make sure that terminal in the connector is good at the switch, and if so, replace ignition siwtch.