Generator question for electricians

I used to own a TIGER brand generator 2700 that was supposed to be a 2KVA generator. It worked well and powered our airconditioner, power tools and jug etc, but would not run our High Tech battery charger because of the electronics requiring pure sine wave power. On one ocassion I found that the 19 amp extension lead had been very hot and there was some melting of the plastic factory fitted plug. This only happened to me once and because I didn't know what had be connected to it at the time could not isolate anything. I gave this generator to my daughter and she has just told me that while it was powering 1 light, and television another extension lead suffered melting and triggered the safety switch. As this was only a light loading, have any electricians out there got any thoughts on what the cause may be. I have told them to take it to an electrician for testing. Brian