Very seldom heat would affect a five speed transmission, they just don’t get very hot. There are a few different things that can cause a problem like you are having. Drive pulley will not stop turning, allowing the shift keys to move. Bentinite, grease, is too old and stiff to allow internal parts to move properly. Worn internal bushings, causing shafts to be out of alignment. Before pulling the transmission for investigation, verify the the drive belt has stopped moving, with the engine running, before trying to shift. Post back if you have more questions.