What would cause such a problem in the plug of an extension designed to pass 1800W when used with a medium, intermittent load with no large inrush current?
Could be a NEC 110.2 "use listed equipment" problem, if the extension cord is not UL listed.
Could also be a NEC 110.14(D) "torque terminals to spec with an actual torque screwdriver" problem if the socket was not torqued to spec and the real heat source is the screw terminal.
Could also be cherry-picked selective application of NEC 110.3(B) "Follow instructions and labeling". I have skepticism both that the extension cord is rated for 1800W or heater loads, and that the heater instructions say "OK to use with extension cords" and "OK to run unattended". I suspect it says the opposite, in boldface.
Cadet makes 750W baseboard heaters which hardwire in, which would eliminate the extension cord trouble, and are rated for unattended use. This is the way to go.