There are some units that use simple mechanical thermostats and either thermal-expansion type or millivolt safety valves. The later converts the heat from the pilot light into a tiny electrical current that holds a gas solenoid open. If the pilot light goes out the pile cools, stops producing power and the gas valve closes.

These units would also lack a blowers to distribute the heat. Many of these units are wall-mount radiant heaters and fairly inexpensive.

These units are not all that common despite their relative low cost because they heat unevenly, only really heat one room, they are not pretty, and their presence places limitations on what you can place along the wall in front of the heater. Drapes or furniture places in front of them can overheat and ignite.

Mostly you see them installed in rural cabins and lodges where their low cost makes them attractive, there are not a lot of furniture that is likely to catch fire, and aesthetics are not an issue.