In physics, ‘temperature’ measures the intensity of the interaction between the elements which ‘inhabit’ a certain place.
The more energy exists in a certain place, the more intense the interaction. If the place is inhabited by a gas, each molecule is able to ‘travel’ a short distance before actually hitting one, or more, of its neighbors. If the place is occupied by a liquid, the molecules glide against each-other and if we speak about a solid, the components just shimmy together.
The more energy exists inside a place – the higher the temperature, the more intense the interaction between the individual components. And if, for whatever reason, ‘too much’ energy accumulates into a given space the interaction becomes intense enough for ‘change’ to happen. As temperature raises, solids melt, liquids boil and evaporate while gases become plasma.

Adding energy isn’t enough to determine change. Temperature might rise without anything noticeable to happen. Specially when we speak about liquids and solids. If enough outside pressure is applied, the liquid cannot start to boil and the solid stays in place.

Same thing when it comes to a society.
High output societies need a very intense social interaction to make things happen.
To make so many things happen at once… that being the reason for which those societies need to be democratic. Autocracies are too rigid, they cannot accommodate the continuous adjustments needed to ‘absorb’ the huge amount of ‘social change’ warranted by the amount of energy ebbing through the system.

One way to measure ‘social temperature’ – other than the ‘output’ of that society, is to gouge how vulnerable a society is when confronted with a highly infectious disease which is transmitted through direct contact. Cholera will sweep through an entire community which drinks from the same well, regardless of how much contact individual people have with each-other. Covid, and Ebola, need people to ‘touch’ each-other in order to jump from one to another.

But don’t forget to factor in ‘pressure’. And other things specific to each individual ‘place’.
Otherwise the analysis might produce less relevant results.