A heater may be a resistive load but it usually draws a huge current. If the contact between source of power and the element of the radiant heater is bad it will lead to a high resistive connection and that can act like a heating element in its own right causing your problem. Note say you have 12 amps going through the radiant heater. If your contact is poor at any junction and the resistance of said contact starts to rise way above zero good old heat dissipation comes into play as you begin to get a volt drop across the contact. Once you get a reasonable voltdrop at a decent current P= VXI so 12 amps and say 12 volts drop and you got 144 watts of power to have to go somewhere as heat. You can play with the numbers and see where it goes. And by the way this is not DC so it is an inductive load to boot.
To give you an idea i experienced this very issue during my time in the army. We had an electrical panel that we hooked up to two huge diesel generators.
Well one day the "sparkie" and i (radio mech) had to replace the main circuit breaker and all went smooth. That night we had to run the generators due to local supply being out and on returning to our cabin we passed by the generators to check on them before retiring. When we opened the panel door the breaker, whose housing is made of bakelite was glowing red. We immediately started our second generator (yeah you know the army standby genny) and cut over and shut down the first one and its panel. Let the breaker cool and we found the only issue was the tightness of the screw where the wire came into the breaker. It had not been tightened down by one of us properly. Its not always easy to get the right tension on those screws and they a real good source of this kind of issue. It fixed the issue and we return everything to the way it was and went to bed. Lesson learned.
I am amazed that from what i have seen in offices and businesses in North America with the 110v flat pin contact arrangement that there are not many more fires as a result of not only poor contact but from overloading or using under rated extension cords. If basic literacy is an issue then electrical literacy is even a bigger issue and people tend to think if it has a open pin heck plug it in. Even appliances i note are sold with marginal gauge wire such that running a simple thing such as a vacuum cleaner leads to a situation where that cord is warm after say 30 minutes of vacuuming. Once again we have two issues at play, where they manufactured and how, and wire gauge to meet a price point.
Just a cautionary make sure your smoke and co2 detectors are working. If you want to test your co2 just open a small propane appliance near it. Dont ask me how i know ask Linda.
My advice would be upgrade the extension cord and cut off both heater and cord and fit your own receptacle and plug with proper joint. Be safe and if in doubt dump it all and get new but check the quality of new. I am not a fan of molded on plugs or receptacles. Have you seen the joint in those things ? Often its just a spot weld. One really needs to get all the conductors joined when a connection takes place not a few of the strands. One is looking to keep not only continuity but also the cross sectional area of the conductor going through the joint. Otherwise you have a voltdrop potential event.
Were I in your neck of the woods i would be there like a shot to help you out. I nearly lost a good friend when i was younger to a radiant heater issue being left on overnight and a sleeping bag being used as an extra blanket slid off the bed and began leaning against the heater. Fortunately his dad woke up before it was too late when the smoke came pouring into his room. Trouble was averted but it was so so close.