My cold water pipe is frozen under my kitchen sink. I don't have a basement or crawl space..how do I thaw it?

You have two things to be concerned about: the frozen pipe and whether it has burst because of the ice. Until the pipe thaws, you won't know if there is a split in the pipe. Best thing to do is turn off the main water valve (not the one under the sink, but the whole house) before you thaw the pipe. Then open a faucet in the lowest part of your house (basement or first floor) and another one or two on the highest level. This will drain the water out of your plumbing system so no more can freeze. Then heat the pipes that are frozen with a hair dryer; you are risking a fire if you use a propane torch or other open flames. Turn off all the faucets and carefully turn on the main valve. If you hear water running in a wall somewhere you know you have a burst pipe and can immediately call a plumber. IF you don't hear anything, chances are you are OK. I've been through this, and no one told me to turn off the main valve. Fortunately, I was home when the burst pipe thawed. If I hadn't been, the water would have been running for 8 hours before I got home from work and would have been a disaster. Next time leave both the hot and cold water running at a trickle during cold weather. The water moving keeps the pipes from freezing.