You are right on radiator heat. Thats what we had on the farm, 100 year old home, no spiders but lots of mice. I had traps sent all over the house. My dog would hear a trap snap shut and off she’d run checking the traps. I told my dad that those dam mice would do square dancing in the dining room.The house was in good condition, wood floors etc. Radiators in every room, but the mice could find very small spaces to get in the house. Should have had a house cat, but hubby was not a cat friendly kinda guy.
However on the downside it is not fun to have mice turds in your kitchen drawers, empty them all out, wash everything, and wash the drawers with Lysol. Ugh.
So far a patch in the kitchen wall from inside and more patching on the outside has kept them out. Oh if it will just last. I really don't want them in the house.
Maybe you can find where they are getting in? I know they can squeeze through tiny spaces.