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.
I have been considering newer construction materials and the trouble is that most of the material available online is either research papers or companies selling it: both of which only talk good things about it.
I liked one such tech and intend to seek and meet people who are living in houses made using it. That should definitely assuage my doubts.