Thats a pretty good idea, maybe you could try making just a simple frame to hold the cup and an usb extension cable?
IF you're going to print it with a Reprap, MakerBot (or a 3d printer using the extrusion deposition method) make sure to use ABS instead of PLA. The ABS softens at around 90 degrees C while as the PLA is going to be about 50. I'm saying softens, not melting

Give it a try and let us now? You could post it on
http://www.thingiverse.com/.
I'd love to make me a coffee/tea warmer for the winter haha.