If its a shower pump you should not be using it for the whole house, shower pumps are for errr showers ! ie both hot and cold run together as the manufacturers dont expect just the hot or just the cold to be run in a normal shower, whole house pumps can do just the cold or hot, did you buy the pump yourself or did a plumber put it in ?
Originally there was a stuart turner fitted of same design so replaced with grundfos. I called grundfos about it and they said its normal for it to get hot. They didn't state how hot though.
Whole house pumps have an auto-bypass fitted, which allows minimal circulation on the end of the pump not being used to avoid overheating. If it's getting hot I'd phone grunfos again and check that the pump you have is designed for whole house pumping.
What model is the pump, should have it on a plate on the top of the pump?
Technically shower pumps by their very design are for showers only as the others have said and both outlets are open at the same time but according to their MI, the STN pump can supply other outlets in the bathroom so if they have confirmed that the side not in use gets hot by design then there's no reason to doubt it IMO.
I would send them an email to get that in writing though just in case it fails given it's over £400 worth of pump.
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