There are microcontrollers which use 3.6V as the logic/power, right?
I also think that the 'grey area' (I think it's called) for logic starts at 2.2V or something, so you should be able to get away with it I guess. Haven't really tried using small batteries with larger voltage applications, but it will be interesting to know how others do this.
Couldn't you use 2 of these 3.6V in series, also?