frozen pipes

i wanted to take a shower this morning but the water was hot. too hot. no matter how i turned the tap, it didn't seem to cool. after a while, realisation dawned: the cold water pipe must have frozen overnight. great. on the plus side, i still had warm water! and after a bit of research, the rest of the cold water pipes seemed fine, it was just the one near the northern-facing wall that was an issue. and that pipe that drained the bathtub - this morning's scalding water is still there!

the question now is what to do. apart from the whole washing issue (luckily, the gym's across the street), what will happen when the temps come back to normal? will the pipes burst? and is there anything i can do in the meantime?