Using the threshold of a FET as a comparator is a very questionable design practice. The threshold voltage can vary quite a bit, even for a specific FET. It’s impossible to guarantee a consistent input to output transition.
The reason you don’t see a sharp transition between output-high and low also relates to the FET near-threshold behavior. As the FET gate voltage crosses over the threshold, the FET is being biased in its linear mode, so the output makes a gradual transition as the temperature increases, rather than the sharp transition you’re looking for.
Strongly suggest instead that you add a comparator to the circuit, like an LM339 or similar. Falstad has a comparator model in its library. Then you can set a precise threshold that will snap the output state to a definitive level.
One more tip about Falstad: you can create a link to your simulation and add it to your description, so that other people can run it as well.
Related: Why is there a resistor in this circuit?