If you leave them floating, the tiny amount of capacitive coupling to other toggling lines (or any electrical noise pickup) can cause them to toggle also, quickly flipping the state of circuits inside and charging and discharging parasitic capacitance and thus increasing power draw.
The greater problem however is that if an input is not pulled one way or the other, it could remain in a zone where
neither of the transistors it is connected to in a totem pole configuration in the IC is totally turned off, so both are conducting a little, so it wastes power. Consider this inverter diagram from
Wikipedia:
or here's a 2-input NAND gate:
If input B is high so it's trying to pull the output down, and input A is in the middle so both A transistors are conducting a little, there's power waste. Ideally things are either on or off so that if there's no load, there's no current either.
The current shouldn't cause enough heating to damage anything, but why waste it.