Build your pyramid on a coal deposit
There are actually quite a few fires in coal deposits that have been burning for a very long time without human assistance.
The Guiness record holder for longest burning fire is in Mt. Wingen (a.k.a. Burning Mountain), Australia, and is believed to be 6000 years old.
Brennender Berg, Germany is called Burning Mountain by the locals, since its coal mine was ignited in the 1600's.
Another interesting case is the mine fire in Centralia, Pennsylvania, USA, which has been going since the 1960's.
Petrol pipeline
If there is a source of petroleum nearby, you could run pipes underground into the pyramid. Inside concealed fixtures could feed it into the fire. You could even use valves to increase the flow in bursts, to give the appearance of signs from your deity when it is asked questions.