There are several reasons that your 13 double over transmission will not go into gear. The most common reason for the transmission not going into gear is the shifting linkage is disconnected.
The year, make and model info would help.
a blown transmission they are known for that expect a $1200 rebuild
drop the transmission pan and change the fluid and trans filter
use trans tune made by seafoam
You need to use the clutch and the shifter smoothly together!
The most common reason for an automobile transmission to shift hard is low transmission fluid. Make sure the transmission fluid is at the appropriate level.
If you have a pickup that has a soft clutch and its harder to shift gears you probably have a problem with your transmission. You should check your transmission fluid, make sure its full, and if that doesn't help you will have to take it to a mechanic.
Sliding Gears in a transmission are straight-tooth spur gears with a taper (also known as a lead) to make engaging easier. Helical gears are mostly used in a transmission because spur gears produce gear noise and have a great strain on the teeth of the gear since only one tooth can be in contact at any given time. But because helical gears cannot be taken out of mesh, spur gears are used for the reverse gear because reverse spins the opposite way and cannot be in constant mesh.
Low or bad transmission oil, bad transmission solenoid, vacuum line issues, worn transmission gears, bad torque converter.. all possible reasons.
sounds like one of the valves in the valve body is sticking when it gets hot (metal expands). Sounds like a Ford automatic overdrive to me.
have someone change gears, while not running, and make sure the linkage from the gear lever, whether automatic or not, is moving the linkage for the transmission itself. if the linkage is moving on the trasmission, then its probably in the tranny. also make sure the drive shaft is working (runs from the transmission to the rear differential).
a faulty torque converter, faulty fluid pump, broken input shaft, worn forward band/Worn clutches/Low fluid level