Rational or not, I looked at other solutions. Heated grips, piping coolant through handlebars, hand guards, windshields - these would help, but while fun to implement and shop for, they don't warm your core.

But alas, I finally gave electric heat a try this Fall - in the form of a battery-powered base layer. A quick skip to my conclusion:
I dig it. I recommend it.
The power source is this little lithium-ion battery pack that you charge with the provided wall wart. When all the lights are lit, it's charged. Sweet.

It keeps my core warm, and my arms and legs get colder far slower than before. I've only used heat settings 1 and 2 (out of 4), and I find 2 to be rather warm. But the best part of this product? Battery life. On this battery's maiden voyage, it heated me on setting 1 for over 6 hours. I haven't tried a marathon run with heat setting 2 but I have a feeling I won't be disappointed.
The only negative I've found is that, if I'm in just the right position with just the right thickness of clothes on, the layers press the heating element against my skin firmly. If this happens for a prolonged period of time, it becomes quite irritating...
Want to try it? It's the Longmen Shirt from motorcyclegear.com.