we can be expressed as algorithms
Wow, do you have any proof of this wild assertion? Has this ever been done before or is this simply conjecture?
a thermostat also has an internal world
No. A thermostat is an unthinking device. It has no thoughts or feelings and no "self." In this regard it is the same as LLMs, which also have no thoughts, feelings, or "self."
A thermostat executes actions when a human acts upon it. But it has no agency and does not think in any sense; it does simply what it was designed to do. LLMs are to language as thermostats are to controlling HVAC systems, and nothing more than that.
There is as much chance of your thermostat gaining sentience if we give it more computing power as an LLM.