DaveC wrote:
Have a 50-year-old (?) natural gas wall heater in my apartment.
Thermostat is connected to gas valve in heater by 2 wires. No
evidence of transformer or low voltage (ie, 30 vac) on the wires.

Symptom is that the 'stat won't open the valve. If I short the
terminals for just a second, the valve opens, and shuts at the
appropriate temperature. (I since have read that it's not a good idea
to short those terminals together; it could damage the valve, or some
other component.)

What replacement thermostat should I be looking for? All I see are
multi-wire types that require a transformer voltage. Will any
mercury-bulb type work? (That's what the old one was.)

I'm also curious where the voltage comes from to operate the valve.
Is this generated by the thermocouple / sensor next to the pilot
flame?

As you guessed, the voltage (250, 500, or 750 millivolts, MOL) comes from
the thermopile heated by the pilot flame. Most systems are 750 mv. If you
have a voltmeter, measure the output of your thermopile.

Use a thermostat designed for millivolt systems (usually the specs will
state). Many battery-operated programmable thermostats will work, too.