If you stop the key and wait before turning it again, it's possible that the sensor in the head is warming up enough to close and allow heat. There is a delay from a cold engine, but it shouldn't be more than a couple minutes. As soon as the engine begins to warm up, it should start blowing heat. It certainly sounds like your current problem is the CCU. I'd put the original back in and troubleshoot the heating issue. Try setting the temp wheel to max cold and see if the fan turns on. If it does, you know the delay is probably due to the temperature sensor in the head.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]