Yes, that box is missing the neutral.
The National Electrical Code did not add that requirement until 2011.
Smart switches require a source of constant power to work. Therefore, they trickle a small amount of current on the neutral while they are working. They used to trickle this current on the equipment ground which was decided to be unsafe by the code making community. However, these older style switches that do not require a neutral are still available and can be installed in your situation.
Return the switch you have and look for a "no-neutral required" type of switch. Depending on how "smart" you want your switch to be, you can find occupancy / vacancy style switches that do not need a neutral and use the equipment ground instead. Similar to this one.
Harper is correct in his observation that thermostats use a low voltage system that is powered by the HVAC system through a transformer. You cannot get a neutral here.
Good luck and stay safe!
This is a switch loop. The unpainted whitee and black are always-hot and switched-hot.
You don't have neutral here. Further, the extra hot wire can't be on this switch.
Notice how the hot and switched-hot on this switch do not have any paint on them. They were added later, and are a switch loop to a different circuit. They were installed before NEC 2011 took effect, because that requires neutral on a switch loop. That would be the neutral you need and do not have.
The paint-speckled hot, however, is a dangerous interloper. It is stealing hot from this circuit, but returning neutral on another circuit, causing that neutral to be overloaded*.
Further, that invasion is totally needless. There are plenty of wires back there, so some must surely be hot for its own proper circuit. This needs to be fixed, by a pro if necessary.
Regardless, given the availability of power here, the switch loop might be "flipped", so the power at the lamp is not used by the lamp anymore, and the power comes out of this box. If that were done, the two extant wires would become switched-hot and neutral, and you would be able to install a smart switch here.
Best Answer
TL;DR Switch Loop, No Neutral
You have a switch loop. With a switch loop, power goes from panel to fixture to switch, instead of panel to switch to fixture. That is perfectly safe, but the problem is that you end up with no neutral at the switch. A neutral is simply unnecessary with an ordinary switch. But a neutral is required for many (not all) smart switches, timers, motion detectors, WiFi switches, etc. Current code requires a neutral (or an easily added neutral in conduit) at most switch boxes. But older houses (like yours and mine) have plenty of switch loops.
White is usually neutral. But in the case of a switch loop using standard /2 cable, white is permitted to be used as hot or switched hot. Actually, it is supposed to be hot, not switched hot, but that is irrelevant to this discussion. Since your switch has black and white wires connected, it must (unless there was some major code violation going on) be a switch loop. If it was not a switch loop then it would have two non-white wires (typically both black, but not always).
End result: You will either need to run a new cable or find a smart switch that specifically does not require neutral. A smart switch needs power. Short version: it can get power from battery (needs changing), capacitors (very limited), leak through hot (works great with incandescent bulbs but not with most LEDs), neutral (ideal, except when you don't have neutral at the switch!) or ground. You can't simply use ground as neutral - it will probably function but it will not be code-compliant and is therefore not a good idea. There are some switches actually designed and listed to use ground for power, but the amount of power is limited and this capability varies by brand - and by model within each brand.