voltage - Are devices damaged by high current, or high temperature?

I'm wondering if electrical devices are damaged by the current or by the temperature. Imagine we have a little device with a maximum input current of 500mA. I'm sure that if we subject it to 1A or 4A it will become very hot and probably explode. The question I'm asking is whether the high temperature induced by the current is the principal cause or it's the high amount of current that is the cause. I'm wondering if we cooled the device at -230 Celsius (we're accepting that it's still working) and then we applied that high amount of current would it survive?