When you get the heat water is being passed through the water control value. This valve is powered with the key on and grounded by the push button controller to stay shut off.
During those moments of heat (BTW heat coming from the outside vents is the way it works the center vents close off during normal heating; the center vent air will be warmed slightly but not like the side vents), you are probably loosing the ground signal from the pushbutton controller.
Since its intermittant, I would try a jumper ground till you can be sure it has or hasn't made a difference (be sure you ground the right side). The ground wire is the YL/GN wire. The BK/PK is hot from fuse# 7.
There is another possibility with 124 chassis. If you are using the temperature controls (setting in the white region of the knob), the temp is being controlled by mixing hot air with the A/C air (the refrigeration system always stays at maximum efficiency). During this mixing the water valve is pulsed (open and closed) to control the heater core temp. On 124 cars the heater core flow rate is very dependant on engine speed (and auxiliary water pump). A condition can result if the aux water pump is failing.
It goes like this: You sit at a red light with the engine idling on a moderate day, the car has reached temp control (normalized), the heater valve is told to increase water flow because the core is cooling and mixing is required, the water isn't flowing so the valve cycle is held increasingly longer open, and now the light turns green and off you go. The valve is in maximum open cycle and the increase in engine speed rushes hot water in before the controller can regain control. This causes the effect you describe but it will correct itself once constant speeds are regained. More than any earlier chassis the 124 system uses the aux pump to keep flow rates constant. This is not a condition we see much in Florida as mixing is hardly ever called for during the day.