Hello , here to try and help you to understand what may be going on .

This is a classic symptom of a failing starter, you should have the cable tested also because it is also a known failure. The fan module is also a known failure located in the p/s wheel well. I will recommend replacement due to these parts being such problematic and common failures.

the starter will have to be tested, the ignition switch is a known failure if you notice the dash lights working intermittently and vehicle not starting intermittently you may have an ignition switch problem. Although the starter will need to be tested to rule out replacement and vice versa.If the switch is good why replace it. It can only be tested using a known good switch in it's place. By removing the switch and placing a known good part and testing the function will let you know if it needs replacement. To test the starter you will need to apply direct 12v to the starter solenoid which is very difficult to reach.The fan module is a common failure for you symptoms and is unrelated to the starter.
The cable is a known failure if your gage reads different than the actual output at the cable itself (eg. Below 13.6V while engine is running)
The least expensive part to replace and the simplest repair/check is the ignition switch but as you state when the engine is hot and does not crank usually a sign of a failing starter.