"Phil" wrote

"If you can insulate the pipes in any way, the water will stay hot &
the wall not...."

Nice idea Phil, but this will mean chopping a significantly larger channel.
I am reluctant to do this, as the route passes close(ish) to a window
opening.

Having said that, I have some offcuts of heat resistant matting only about
2mm thick (used to put on the dining table under the table cloth for
protection) - should be able to make room for that.

Good call

Phil