Someone with more experience can correct me, but I doubt you’ll get enough energy transfer via the radiator in the house.
I think you’d get a lot more mileage out of an attic fan. Keeping the attic cooler during the day will slow the heating of the house.
You may also want to take a look at better roofing materials. There are roofing materials designed to reflect more of the sun’s energy as well as radiate what heat does get absorbed better than others.