Cold water pipe frozen, hot water fine
If you have access to the frozen pipe or the cavity in the wall/floor where it is you can use a hair dryer to heat the air around the pipe (a cheap hair dryer blowing up into a wall from a basement unfroze a pipe within minutes for me).  I would not apply high heat (e.g. heat gun) to the pipe directly as you can cause the water to expand and damage it.  If you have direct access to where the pipe is frozen, applying a towel soaked in hot water is another option.

If you own the home, look into insulating the pipes and the cavity they are in.  If you rent, inform the owner of the problem.