The arduino processor normally runs at one constant speed determined by the frequency of it's oscillator (16Mhz for Arduino) no matter what code it's running and it's always running some code, there is no halt condition in normal conditions. A wait or delay loop is no difference then a calculation loop as far as power consumption goes.
The AVR chip does have some special sleep modes where the chip is put into a low speed/low power condition and waits for some kind of interrupt to 'wake-up'. But other then that it's just a constant speed device. Now a chips heat generation will be effected by how much current is being drawn by external components wired to it's output pins, so there is power/heat variation there.
Lefty