I do not think you can overheat the motor by closing all the vents. If it was indeed the blower motor that went, it was probably ready to go anyway.

I replaced several blower motors in my old Volvo but never had to change one in the Benz. The Volvo problem was recurring and had to do with a problem of moisture getting into the motor housing and causing corrosion. If you can get to the blower, try turning the fan by hand to see if it offers resistance. It could be that it ran out of lubrication or has some corrosion, if that is indeed the problem.

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