Small scale heat tape project -- is this possible?

Thanks for all of those links -- lots to think about! Steve, yes, the area in question is within my recirculation zone, but I do not want to have to get up every two hours at night and run the hot water. It is no fun to stand in the freezing cold and dark for five minutes, hoping I do not wake DW. I want the tape to do the job silently, and then I will recharge the battery in the morning.