...the higher the frequency (up too a point with the material) the more efficient was the transfer and the less copper etc needed.

Yep. Have a look at a switchmode power supply or a DC-DC converter/inverter. The transformers run at HT and very high frequencies and they are tiny by comparison, typically not much larger than an output transformer in a pocket transistorised radio.

Even with diathermy machines, the current running between the surgeon's probe and the earth plate stuck to the patient's bumcheek is tiny and the frequency is so high that the patient's heart and other muscles don't react to the current despite the voltage being at something like 5,000 volts. I would not have liked being the lab rat they tested all that on. Diathermy machines have two functions: cut and coagulate. I don't remember what changes to go from one to the other but it is a simple setting on the machine's front panel.

Have a look at the images in this one, the transformer looks like having some bubbles!

http://www.ebay.com.au/itm/Retro-KRIESLER....

Heat damaged back panel

http://www.ebay.com.au/itm/KRIESLER-VALVE-RADIO-MODEL-11-81....

Heat damaged top left

http://www.ebay.com.au/itm/Vintage-Kriesler-Radio-Made-in-Sydney-in-1959-/251573756119....

Most models of plastic radio suffered a fate like this. Even though there were plenty of ventilation holes in the back of most of them it was in effect only one set of holes so there was no way for convection to assist with removing heat. A better way would have been to have holes in the bottom and then on the back panel only have holes on the top half to create a wind tunnel effect similar to how laptop computers are designed. Rectifier and power amplifier valves in particular give off a lot of heat and these are usually close to the warm transformer. It is bound to be on the side of the set where any meltdowns occur.

Don't be too worried about the wax you can see there. All transformers can spurt a little when a radio like this is running on a 40°C day. When it is far more profuse, more often a charred colour and gives off a sharp stench, you will know there are problems. Some manufacturers dipped their transformers in pitch instead of varnish or wax. From memory, HMV was one who sometimes did this. When one of these transformers packs it in the smell it creates can have the police roping the whole street off by comparison.

Thanks Brad for the explanation, hopefully when I knew more about these radios, I 'd feel more comfortable with heat.