I am not familiar with your car but typically older MB has problem with Automatic Climate Control Unit. With age it would develop cold solder joints causing all kind of issues. What happens is that with cold joints the current do not flow as suppose to be and cause malfunction in the climate control system. One of the remedies is to take the ACCU out and resolder all the joints, very easy if you are electriconically inclind. The expensive route would be to replace the unit with a new one or rebuild one.
Another cause for your problem could be Monovalve, the diaphram on the valve become britle with age and finally rupture causing the heater issues. This is the valve which is responsible for the flow of HOT water into your heater core and if the diaphram is ruptures it can totally or partiall block the suplly of the Hot water. There is a repair kit for this, easy to fix. Do a search for your car, typically it could be found between the firewall in the engine compartment.
The last but not the least could be a vaccum leak causing the malfunction of the flow of the heat, when you accelerate the vaccum increases compansating the leak and heat start flowing in.

You can start looking into the above steps one at a time, once again I do not have your car so use these as a guidence and not absolute.

Hope it helps.
Thanks

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87 420 SEL
Looking for a nice mid 80's MB diesel.
87 BMW 528e (Sold)
99 TOYOTA 4Runner
1989 Honda Accord (Sold)
1988 Honda Accord (Total)