@louise1948_29
Hi Louise,
Here is what you must do.
* Check amperage of heater - look on plate on back of heater and it wil state voltage and amps.
* Check amp limit of extension chord.
* Check amps of circuit - look at fuse or circuit breaker for outlet - important to check rating of circuit as some one may have incorrectly used a higher rated fuse/circuit breaker. It is strange that the fuse/breraker didn't trip.
All three MUST match or you could burn your house down.
You know some circuits may just be wired for lamps. So check!!!!
Having done all the above yes you may rewire the plug but make sure you get the polarity correct. There should be a little diagram, etc. with the replacement plug.