The plug or socket is part of the electrical supply, not the intended heated laundry space. Unusual heat, scorching or a burning smell there needs attention.
Understanding this situation
Do not test it repeatedly by touch or assume that all warmth near a dryer is expected. A damaged connection can remain hazardous even if the drum still turns normally.
A useful next step
Stop use and isolate safely without handling wet or damaged equipment. Arrange appropriate electrical and appliance advice. Do not swap adaptors or uprate a fuse simply to complete another load.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.