Can heat make you lose your eyesight while driving for a long time?

Heat. Unlikely. Your eyes may blur due to dry eye if you drive a long time. Take frequent breaks, and use artificial tears when driving. If you are in the heat for a long time, heat stroke or heat exhaustion may occur. Drink plenty of fluids, and get some rest if you do not feel well.
Yes. Prolonged visual concentration may result in suppression of the normal blinking pattern which can leave the eyes very dry. In some individuals this can result in mild swelling of the surface of the eye ( the comea) which can persist several hours until the eyes have been allowed to close and rest for a period of time.