The cryocooler technology (say, to a few kelvins) has proved hard to get ready for space. For example, out of the 10 or so technologies that were judged most risky for JWST, the 6 K cryocooler for the MIRI instrument was the last to be judged ready for space ("at TRL 6" in the jargon) (http://www.stsci.edu/jwst/news/2007/jwst-passes-tnar).
Despite being judged ready, the JWST cryocooler has proved very challenging to build. The effort now has frequent reviews with the director of JPL (and a high-level counterpart at NGST), and tens of engineers are now working on the system.
Part of the problem, as I understand it, is that the heat has to be taken away and radiated at a site distant from the IR detector. This requires a large structure, and a deployable radiator. This large structure can't leak much heat back into the spacecraft bus or instruments, and must not be disturbed by the vibrations of launch. Additionally, vibrations of the cryocooler must not affect the telescope optics (2 micron resolution).
You can tell that these requirements are fundamentally opposed to each other ("be large, don't vibrate, don't touch anything else").