As I was typing, invar and benfingland beat me to it. I hate to waste keystrokes, hence my reply.

I agree with Mr. invar and Mr. benfingland. This sounds like you have a very simple burst heater control valve. Less likely, heater hose leak. There are two hoses that attach to the heater core via two hose clamps. This is very easy to see on the firewall in front of the drivers position. One hose goes into an engine block fitting under the intake manifold around the #3-4 cyl location and the other one goes into a metal tube behind the block. One of the hoses are cut in two for the on-off heater control valve. With a good light and dirty hands and you can follow the hose path and see the heater control valve

Replacing these hoses and heater control valve are a pain but very doable for a persistent shade tree mechanic. The Volvo brand (discounted) parts are probably $40-$50. Otherwise get the car to an independent Volvo shop or, I hate to say, dealer, and far away from the shop it's at now. A guess, parts and labor will run about $200.

Preventative maintenance is very important. Considering the age, the all coolant hoses, the coolant overflow tank, the cap, and the radiator should be replaced by now. Also see Brian S's post and the FAQ conserning an adding a low coolant level sensor.
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Tom F '95-945na, '94-944na, lien holder on a '95-944Ti, RIP '78 244