I'm confused what you guys are saying when the "shutter was not installed" and "it closed in the winter position ".
All the 034/036 I ran had a window (shutter)in the top cover between the cylinder and air box in the top cover partition.
Plus the back cover that housed the air filter had another shutter/window that could be opened closed for the air intake through either the grill in the cover from the lower back or at the top screen.
Also for the winter operation of the heat transfer from the cylinder could only be made when the special winter back cover with the rubber flange was installed.
This rubber flange sealed the gap betwern the 2 top covers.
So if this winter cover was not on the OP's 036 there is no way it would overheat no matter if the shutters were opened or closed.