My experience with heat and Elise was different. I never detected any burnt smell, and while the tubes were often hot, as they are on any tube amp, the chassis never seemed unusually hot to me. This a picture of the bottom of the Elise I'm selling, and it doesn't look like any internal damage was done after a year and a half of usage.. I have not opened it up, so don't know for sure what it looks like inside.
I am happy for you, if yours didn't suffer from the heat.
Mine has melted plastic (or vinyl) resister/capacitor lead coverings, many resistors got so hot that you cannot read the color bands anymore (and certainly appear to be physically deteriorating from the heat.
Later production amps have several good sized holes drilled in the board seen in your photo, to allow heat to rise up and pass through this area. That tells me FA is aware of the heat buildup problem.
Mine still works, too, but for how long? In my case, I do wish I had added a small fan to carry heat away.
Using the external Transformer, was the answer to keep mine from completely failing. Deck and innards MUCH cooler when not using the internal transformer to supply the heater currents.
In your picture, you would know a lot more about the internal condition, by removing the bottom panel and taking a closer look.
I paid the small intro price for Elise and certainly got my moneys worth of enjoyment out of it.
If I could have changed something about its design, it would have been a Transformer that was not enclosed under the cover. Mount he Transformer on top deck where it can dissipate its heat in to the air and keep the innards much cooler, as in the Glenn designs (and most classic 1940's/50's designs)...many air holes along the sides as found in the Darkvoice, would also have helped...if not these two items, a small fan should have been mandatory, IMHO.
Cheers.