The library here is mostly used for individual study rather than access to books, though there are plenty of books available just in case. But most users of the library sit still in individual seats at desks to work.
The heating system is centralised and exudes warmed air from grilles. Presumably
there are thermostats to maintain an average air temperature that is too hot for half the users and too cold for the other half.
I propose organising the library as a temperature gradient, so on end is the cold end (appropriately signed and marked, perhaps with blue desks) and the other end is the hot end.
The heating vents provide hotter or cooler air according to the endedness of their venting.
Instead of a thermostat, the temperature of each vent is controlled indirectly by the users. Person-sensors detect the distribution of persons in the library. If there is an excess of people at the hot end, then the entire space is warmed a little. If people are clustering in the middle, then the cold end is warmed a bit and the hot end cooled a bit. Basically the system aims to use heat balance to encourage an even distribution of people through the library.
There should be a pair of buttons on each desk, marked "too hot" and "too cold". These allow a reader to signal to the system their discomfort without having to get up and find another desk. There could also be little illuminated signs on each desk, so that the system could respond to a button press by lighting up a "desk free this way =>" sign, rather than changing the temperature of that area of the library.
There should also be a "sit tight" sign that lights up to indicate that the system is going to adjust the temperature for you.
The system only needs: buttons and signs on each desk, complete person-detection coverage, and hot/cold mixer valves at each heating outlet. And a clever software system to regulate everything.