It's best to let it warm up for a minute or so before applying a heavy load, but beyond that short runs aren't particularly bad. Most of the wear (for any gas engine) happens during and soon after a cold start rather than during continuing operation once up to temperature. If you do a lot of short generator runs, it would be a reasonable idea to change the oil in it more frequently than otherwise.
(Not intending to open too big of a can of worms, but there are several good ways to make coffee that don't require using the generator....)