I'm a sparky....
The risk I see isn't overloading. That's what your circuit breakers or fuse is for.
A lot if fires start because of bad connections. Plugs not in properly or loose. I'd never connect a power board to another power board. I would connect a power board to an extension lead no worries though. Really you just need to bite the bullet and get another outlet installed. It's the safest thing to do. Power boards often sit flat and get dusty. Dust can be conductive at times and result in fires also.
Thermostat will work with lots of connections. Not sure what that was about lol.
i was going to add my 2cents as my dad is a sparky, but it seems Snowman beat me too it. also don't use double adapters, i was lucky to have a sparky in the family had dad change all my points from singles to doubles or more depending on the room only cost me a trip to bunnings