I really think you're barking up the wrong tree here.
standard shower protective devices are pressure sensor / flow sensor, over heat cut out, and pressure relief valve, or equivalent (eg an electronic control would presumably cut out if the electronic control failed) any shower without these (or at least 2 of the 3) would be a trading standards job IMO.
and shower elements will be nichrome, which have a temperature coefficient of resistance of
0.00017, so even if it's at 100degrees above it's starting temperature it will only increase the resistance by 0.17%. heating elements wouldn't be a lot of use if they were made of a material who's resistance increased that significantly as their temperature increased.
So a shower is very unlikely to operate for long while seriously over heating, and an overheating shower element won't draw any significant additional current anyway, so it's irrelevant to whether overload protection on the circuit would be required IMO.