The monkey could be naturally on fire because of it's species, or it could have been artificially set ablaze by somebody/something. If artificially set on fire, then it probably won't be looking like a monkey for much longer.
There are several species of naturally burning thermomonkeys. They are located mainly in volcanoes, the Sun, and the alley that runs behind your house. The most common thermomonkey is the Pheonix Chimp, simian infernus.
The Pheonix Chimp derives it's name from the fact that it is capable of flight, though it has no wings. It's flame burns at around 10,000 degrees Fahrenheit, but has been recorded as high as 4,815,162,342 degrees. This thermomonkey was on crack and lit the atmosphere on fire. The only way to stop a thermomonkey on a rampage is to put it in an airtight chamber until it's oxygen runs out. Beware, they are dangerous.
Master Bater: It's a bird! It's a plane! Wait...it's...a...
Shirley Gay: ...It looks like a monkey...
Master Bater: ...on fire...? It must be a thermomonkey!!!
Shirley Gay: Look, it's headed straight for the illegal immigrants!
Master Bater: Run! Run little immigrant children!
Beaners: ¡No hablo ingles, señor!
Master Bater: More jobs for the rest of us, I guess.