MD80 Captain reports being dispatched with an inoperative engine driven generator and using the APU generator as the second power source. APU malfunction enroute requires it to be shut down; resulting in a diversion to the nearest suitable airport.

Narrative

In cruise at [FL330] we noticed an APU OIL TEMP HIGH light come on with a master caution warning. We referenced the QRH and followed the checklist for APU OIL TEMP HI; which directed us to shut down the APU. This presented another problem since the right generator was deferred and now we were down to only the left generator. After that we ran the landing single generator checklist from the QRH. We declared an emergency due to the fact we were now single generator and diverted. Next I handed the controls to my Co-pilot and communicated with my Lead Flight Attendant about the problem and we were diverting. I told my lead FA to please prepare the cabin for a normal approach and landing. I then proceeded to contact Dispatch and inform them of the situation and also talked with Maintenance Control. Finally I briefed the passengers. Everything ran very smoothly and had no problem landing. Everyone was very professional and worked as a team. Thank you to Maintenance Control; Dispatch; and the great crew on board. Suggestion: try to get the right generator fixed; so the APU is not running continuously for multiple days on all flights.