Yes, use a switching regulator. They are not all the same, but most are relatively similar. The data sheets can be helpful in discovering the differences. You seem to be concerned about size, efficiency, price (I would guess) after the basics like input and output voltage and package are satisfied. The other thing is how many external components they require.
The efficiency at the input voltage and output voltage/current you need will determine how much energy will be turned into heat by the regulator. With a switching regulator this will likely be 5% to 20% of the output wattage (a linear one could be 250% or more). With a high efficiency regulator you will be able to minimize the temperature rise due to the regulator. However, if you really need 400-500ma at 3v3, that is almost 1.5W that will be dissipated and need to be removed from the enclosure. I have noticed that while the N18 display doesn’t get “hot”, it is several degrees above ambient.
I have read reviews of some of the newer smart thermostats that they read high. Many of them employ a simple offset adjustment, which allows the user to calibrate them. Unless you can figure out a way to get all that heat out (perhaps the fan, suggested earlier) or use a remote sensing device, you will need to figure out an acceptable “calibration” method to get the results you want.