A smaller tent may work in some situations but can also be counterproductive.
Theoretically you can warm up a smaller space , however on the practical side it can also mean that you fill your tent with more moisture .
We perspire/exhale over half a liter a night.
That has to go somewhere. If the night is still or you are all zipped up a smaller fly will be wetter than a larger one because that is where the perspiration condenses.
In the worst cases it will drip on you at best in a small tent you will get your sleeping bag wet at one or both ends and possibly the sides by pushing the inner against the fly.
In any case as I already mentioned, because you are generating wet heat (steam) you end up getting your gear damp.
At high temperatures, say 80f and above, humidity makes us feel warmer than it is, at low temps , between 60f and 20f or so, high humidity makes us feel colder.