I am going to make a few assumption here.
1) It’s the orange plug on the extension lead that is showing signs of heat and not the black plug on the Granny unit ?.
2) The orange flex, is it 1.5mm ?.
It should be marked on the external wall of the flex.
If it is less than 1.5mm replace it now.
Over a 5m distance 1.5mm dia cable should fine, but my own personal preference would be to use a 2.5mm dia cross sectional flex.
This maybe seen as a bit of over kill here, but the Granny unit is pulling a lot of load over a long period of time.
This is when the heat will be generated.
The flex on the Granny unit is of a larger cross section dia and is less likely to become warm / hot.
The black plug on the Granny unit is of the high quality moulded heavy duty type.
If heat is affecting this black plug, then I would have to question the quality of the orange socket outlet.
If it’s the orange three pin plug that is getting hot, then check the terminal connections or question the three pin plug or even the grey outside socket outlet itself.
If the black moulded plug becomes damaged by heat, it is not really designed to be replaced.
After the Granny has been in use for a couple of hours, it is expected that the plug top will feel warm to the touch, if it is hot then some further investigations are needed to prevent any further damage.
If the plugs become tight / difficult to remove from the outlets, check for any signs of brown scorching / witness marks to either the outlets or the pins of the three pin plugs, this is not acceptable.