A frugal way to keep your bed warm during cold night is to use a Japanese hot bottle called “Yutanpo”.
I found the following website talking about Yutanpo :
http://nihonhacks.com/in-the-home/keep-yourself-warm-with-yutampo/
By the way, the Nihon Hacks website has a lot of frugal ideas that i like.
Recommended by H on the Frugal Japan mailing list.