I'm trying to figure out how much power I could generate from a peltier
device from a given temperature difference. With water as the medium on each
side of the peltier, what temperature difference would I need to have to
power a small water pump to circulate the water round my CPU cooler block?

In other words - could a cooling system be designed to actually drive/power
itself from the very heat it is trying to remove? Perhaps convection would
be required to start or subsedise the equation, but do 'we' think this is
possible??

Could this be scaled up to drive a water pump for a small pool, driven by a
peltier that is powered by sun energy heating water on one side in a black,
heat absorbing tank and cold water from the pool on the other side?