Won't be the solenoid /coil on the starter, since you can start by jumpering it on the starter...
There is a relay that sends power TO the starter. The 'starter relay' (on the diagram) is controlled by FOUR switches... HST pedal, seat switch, PTO shift lever and the rear PTO switch. Any one of them, can stop tractor from starting.
Starts fine when cold, not hot... suggest a switch moves a tad after you've run it for awhile. Maybe the HST pedal ?
When it fails, turn key to start then 'rock' the HST pedal fwd/rev to see if that does anything. If no, then NOT the HST switch... only 3 others to try... Same test 'engage/disengage', 'in/out', whatever you want to call it , to open/close the switches. Sounds like one of them is not adjusted quite right.