It may be the defrost thermostat. Some of the older ones would open at temperatures upwards of 90°F, while the newer ones in energy saving refrigerators open somewhat lower, around 50°F. If the thermostat contacts are welded, it will never open and the defrost heater will run as long as the defrost timer allows it, typically 30-35 minutes. A properly working defrost thermostat will cut power to the defrost heater when it has warmed enough to assure all the frost is melted off the evaporator coil. If you can locate the defrost thermostat (after unplugging the refrigerator), warm it gently with a hair drier until it feels warm to the touch, i.e., is 90°F or higher, then measure its resistance with a multimeter or continuity checker. It may be helpful to unplug the defrost heater element to make sure you aren't measuring the continuity through a stray path. The contacts should be open, i.e. the resistance should read infinite and a continuity checker should show no continuity. If it reads as a short circuit, this is the culprit. Defrost thermostats can fail either open or short. Since it appears that the defrost heater in your unit is getting power, I'd guess that the defrost thermostat has failed short.

Another possibility is a sticky defrost timer motor. As noted above, the defrost cycle should go no more than about half an hour. If it goes longer, the defrost timer is the culprit.