I don't think the health of your hair is going to go into the crapper because of one day's use of a little bit of heat. Deep condition well and then use a trusted leave-in and heat protectant. You can even use heat-activated products that protect your hair.
Using a blow-dryer on the lowest and coolest setting is hardly damaging at all. You could also get a rollerset and then brush it out. Steam rollers are a great alternative. Air-dry as you normally would, comb your hair out and then put the rollers in.
There are, of course, other ways of documenting your length progress than using heat. You could do it on wet hair, too.