I don't know what your skill level is, but you can make MORE than a serviceable bow in the time allotted. Wood, once dried quickly, is still soft wood. Performance will degrade quickly. Now, if you don't want that to happen, then do this:
Do as advised, cut you some hickory, shape the bow out immediately, and seal (I use painter's tape myself) the back, ends and fades. Here, you want the bow as close to finish dimensions as possible. It'll dry quicker that a way. Finish out the handle and fades. Trick is to remove as much wood as possible for quick drying.
Now, in 4 weeks, if kept in the house between 40-50% RH, you can then induce some reflex as you heat temper it's belly without fear of checking from the heat. That'll make for a better performing bow. But, you can do better. Depends on how big of a gambler you are. Belly may be hardened at this point but most of your set will come from the back's fibers stretching. Gotto tighten those up as well. A very light heat tempering will take care of that. A backing of some sort will provide some extra measure of confidence here.
Good luck, and keep us posted...........Art B