Yes, what a suprise. A CPU with a TDP of 2 watts is getting really hot. As in, hot to the touch.
My Eee PC 1005HA is getting really warm around the Hard drive area...
somebody want to explain to me why it is that when the system get's really hot, plugged into AC, charging battery, the fan does not spin up, yet when powered by battery, with minimum load and battery drainage, the fans start whining like mad...
Download HW Monitor and see if you can give us exact temperatures. Also, check the ASUS site, their might be an updated fan profile for your system that might fix your issue with it only doing it when its on battery.
check for bios updates also, and check your bios settings.