I was wondering if a 1KW PSU at 400W load generates less heat than a 500W PSU at 400W load? Let's assume that both PSUs are equal and only differ in terms of maximum load.
Really too many variables to say for sure without in-depth information on two specific models. The Transformers, Caps and MOSFETs used in the design have a lot of influence over total heat losses.
Generally though, I'd lean towards the higher wattage PSU running cooler. Heat shouldn't be a make-or-break issue in either case provided both PSUs are of reasonably good manufacture, but the one designed to handle a larger load will probably generate less heat when underrun. (Like I said, this is not necessarily true depending on the components in the two PSUs under test)
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I thought so as well, until yesterday when someone pointed out that if a PSU has for example 90% efficiency, then both (600W, 1KW) PSUs generate 50W heat when they draw 500W.
I know I'm ignoring some factors, but as mentioned above, let's assume both PSUs are identical.
If both PSUs are identical, they necessarily also have the same overall rating and heat losses. That's a bridge too far. It invalidates the thought experiment.
It's near impossible to estimate with a high degree of accuracy unless you have schematics and datasheets on the components on two specific models under test anyway, so I don't really know what to tell you. Generally (though not necessarily 100% of the time) the underrun PSU will generate a bit less heat.
If everything about them is equal aside from output capability, the one running at 40% load will probably produce less heat than the one running at 80% load
HOWEVER
the difference will literally be just a handful of watts. The efficiency difference between 40% load and 80% load is only going to be a couple percent at most. I mean at a 400 watt draw we're talking at a difference of maybe 10 watts from the wall, assuming 90% efficiency at 80% load for the 500 watt unit and 92% efficiency at 50% load for the 1000 watt unit.
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If both PSUs have the same efficiency at a given load (absolute power), then they will produce the same amount of heat. The more powerful PSU will just be better at dissipating it. So it might run cooler but the loss in energy through heat will be the same and in the end the environment will warm up the same amount.
But the better question is, what efficiency do both PSUs actually have under the same amount of load? Standard computer PSUs don't have the same efficiency across the whole range of possible loads, like @w.meri already pointed out.
So ideally you should pick a PSU that is first of all powerful enough for the maximum load that can be expected and second, it should be most efficient at the average load. So if your system usually runs around 150W for example and only sometimes peaks at 400W, then you should focus more on the 150W than the maximum load. And if the 500W PSU has a better efficiency at 150W than the 1000W PSU, you will save not just money on the purchase of the PSU but also the overall energy consumption of the system.
Of course the higher the loads are, the more important the efficiency becomes, but you also have to ask yourself, do you care about your car's mileage for average use or for running at maximum speed?
Efficiency curves etc.
The actual, real world issue is more complicated than this, which is why I keep qualifying my responses.
He didn't ask how two spherical frictionless PSUs would perform in a vacuum under microgravity.
Another thing is also noise. The "bigger" PSU will run quieter, because the fan will spin slower. How much that affects your system depends highly on the brand of PSU and the rest of system. If you already have a noisy GPU or CPU cooler, the PSU won't really make a difference.