No, no, the regular engine driven water pump supplies plenty of hot water to the heater core. The aux water pump is there to help out while the engine is at idle speed - the flow of hot water can get a bit weak then. But when moving down the road, it's quite unnecessary. I had the aux water pump unplugged on my 123 for years and the heater worked just fine.
I understand not having an aux water pump can cause some hot-air-flashes during the winter. When sitting at at traffic light, the heater core cools off due to low water flow. The PBU holds the monovalve open in a (failed) attempt to raise the heater core temperature. Then you put your foot on the gas and move away from the light. A blast of hot water hits the heater core. It's now too hot, and the PBU closes the monovalve. But it's too late, there's now too much heat, and nothing to be done but wait for the heater core to cool down. It's this latter scenario the aux water pump is meant to help avoid.
If there's any consistency to when you get hot air (i.e. after driving 30 minutes on a moderate day), I don't think you have monovalve problems. The monovalve has two positions - fully open and fully closed. (The PBU pulses it between the two to control water flow.) If the monovalve is broken, you're gonna get full heat, and it's going to stay that way regardless of which PBU button you push.
BTW, the PBU on the 124 has built in protection against a shorted out aux water pump, unlike the 123. On the 123 a failed aux water pump destroys the PBU. On the 124 the PBU just kind of shuts down - resulting in the blasts of hot air we all know and (don't) love.
You may question the diagnosis, but I'm about 90% certain you have a shorted aux water pump.