EGR is only to be functional in the cruise power range, it should not be on at idle and WOT, if it is something is wrong with the mechanism.
It dilutes the mixture with an incombustible gas which slows the burn speed and lowers the combustion temperature to reduce NOx formation. To that end there isn’t anything to be gained by cooling it as hot or cool it is going to slow the burn which will cool the combustion temperature.
A common problem with EGR is detonation, but this is really caused by a control failure that is keeping exhaust insertion from happening when it should. With this system the cruise mixture is leaned out so a failure of the EGR to supply exhaust is likely to result in more air being present in the induction system than the fuel system of carb jets or a fuel injection routine are designed for so the mixture falls lean and the engine pings.