The diode will eventually reach a point where the energy inside the cavity is too great and the semiconductor "chip" will begin to deteriorate. This kind of damage creates "zombie" diodes.
Edit: Even if you surround your diode with an impossibly effective heatsink, the gold plated brass that the semiconductor is attached to (or whatever metal that is) and the semiconductor itself are not perfect heatsinks, so heat will accumulate even if at a slower rate.
Edit again: Come to think of it... what metal is the diode "package" made of? Both "canned" and "uncanned" diodes are magnetic...
Basically too many photons are flying back and forth in the semiconductor material causing the mirrors to break. That's what causes almost all diodes to die, they're overdriven too much and as a result the mirrors break.
The first problem is that there are -always- internal thermal resistances IN the laser diode. No matter what you do to keep the case cool (immerse it in liquid coolant for all i care), the inside still heats up despite the case being at ambient temperature.
COD is probably the mechanism that kills most resonably cooled diodes as it is though, and keeping it at ambient temperature will not prevent it. Perhaps cryogenic cooling could limit the problem, but thats probably beyond the scope of the question.