Bread-Bakers v106.n035.11

My kitchen too is drafty so I have found bread will rise if placed in 
my Microwave, not turned on.  I find no need but you could put a 
container of warm water in with the dough if you find it necessary.

Another option can be found at www.sourdoughbreads.com  It is a very 
simple and inexpensive proofing box.  Take a look if you do not like 
the Microwave suggestion.

One or the other should solve your problem.

Happy baking................................Jack