Ryuji's Answer is pretty much spot on, but I'm afraid George's answer is almost completely wrong.(posted 8375 days ago)
Increasing the temperature of a developer doesn't necessarily result in larger grain clumps, at least, not for the reason that George gives. Silver grains do not move about in the emulsion, contrary to poular belief.
If there is an increase in grain, it's for the following reasion: Many common developers contain two developing agents, usually Phenidone or Metol coupled with Hydroquinone. The two developing agents react slightly differently to temperature change, and this results in the overall character of the combined developer changing with temperature.
These 'superadditive' developers are designed to work at around 68 to 75 degrees Fahrenheit. If you use them outside of that narrow band, they may give unexpected results, such as increased contrast or grain, but not necessarily.
Other developers, which contain only one active agent, will behave more predictably with temperature.
As Ryuji implied, testing all developers at all useable temperatures is an almost impossible task, so detailed information on how a particular film/developer combination reacts over a wide temperature range is sketchy, at best.A footnote to this about developers based on Paraminophenol, (eg: Rodinal):
The natural hardening effect of P-aminophenol means that it can be used at higher temperatures, and it's used in special 'tropical' developers, which are designed to be used at high processing temperatures.