I agree that your Volvo mechanic is reaching when he thinks about the heater core -- that's inside the car, after all. If you're getting problems with that, you'd know it as you sat in the driver's seat -- experience speaking.

Start the car in your driveway, let it warm up, and look everywhere water could leak from. I've just diagnosed the problem on my son's 1982 240, which sounded similar -- it would run low on water, resulting in, as he put it "aggressive boiling over." It seems the plastic "overflow" tank through which you fill the radiator has developed a weak spot. It doesn't leak visibly when cold, but it begins to leak from under the tank as the motor warms up and pressure in the system increases. It took a while to find, as it was dripping underneath, onto the bracket that holds it, and then sneaking down the fender liner. There's a well in the middle of the top of the tank, with a matching upside-down well underneath, and it's leaking from there -- I suspect the plastic has cracked where it was heat welded together at the factory. I'll be driving in rubber stoppers top and bottom with "Goop" adhesive smeared all over them, and see if that fixes it. Cheaper than buying one, if it works.