EXO2 makes this excellent lower back warmer:
HeatWave Heated Back Support | EXO2 The Heat Inside
I have the EXO2 vest and will never be without one. Quality is superior to any I've tried and they are efficient without being bulky at all. Check the website if you're interested.
It's not about being warm, per se, it's about keeping the muscles from tensing up. Same reason my grips stay on for three seasons. That said, since I started Pilates my additional core strength has solved another part of the equation.
Cheers,
Ian