CJ, I would find out for sure if the center is supposed to blow first, as the manual clearly states that my '85 300D(w123) only uses the center ducts for cool air. In fact, as soon as I switch from cool to warm air the center ducts audibly close. If the center ducts work when the temp switch is set to cool then you should be fine. BTW, I too wish that heat would come out the center ducts, especially when it is cold. Good luck.

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'85 300DT--215,000 miles
'82 300DT--255,000 miles