No idea about the first one, suspect it's electric but not sure? The belt driven ones are normally running all the time and there is a pressure relief valve that allows fluid to 'cycle' back to the reservoir......however, that's on systems I have worked on and 5 years after retiring is a long time in development. Driving anything takes HP and HP doesn't grow on trees so in the search for every MPG (hence electric PAS) so would not be surprised if they had an isolator clutch but for safety it would need to be bloody bullet proof so my money is on it being electric and all belt systems being clutch less....happy to be proved wrong, happy to learn
As to a cooler, if you pump hydraulics no matter what method you use for pumping you will create heat, heat affects viscosity and that will affect the feel and efficiency of the PAS so simple to fix a cooler inline, it's been the case for many, many years on larger cars.
