Heater Thermostat wiring questions.

I have a gas-fired baseboard hot water heating system with an old mercury thermostat.
There is a 3-wire conductor running from the heater to the mercury thermostat, but only two wires are connected (the Red and White wires). The third wire is not connected on either end.
My first question has to do with what would happen if, when disconnecting and reconnecting the wires at the thermostat end, I got them mixed up and put the Red wire back on the screw where the White wire originally was and the White wire back on the screw where the Red wire originally was. In other words, will it matter if I got these two wires backwards? I have been assuming that the old mercury thermostat is really just an on/off switch, and the circuit is either completed or not completed. So, my thinking is that it wouldn't matter if these two wires were mixed up on the thermostat end.
Is that correct? -- that it won't matter if the wires were put back on the thermostat "backwards"?
My second question is, if I decide to replace the old wire from the heater to the thermostat, what kind of wire should I use? Since only two wires are now being used for the existing thermostat, I assume that replacing it with two-wire thermostat wire will be okay. But, if I later change to a programmable thermostat for example, will I need more than a two-wire conduit to connect the new thermostat up?
NOTE: This is for a gas-fired baseboard hot water, heater-only, system. There is no AC involved.
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It does not matter, its just a switch.

No the existing wiring will work fine, it only needs 2 wires for your system.
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12:17:18 -0400, BetaB4 wrote:

As you've already been told, you can use your existing two wires for a programmable thermostat. The third wire might prove useful, though. Some programmable thermostats can run on 24 VAC provided by the transformer, instead of batteries. You hook up the third wire to the "C" connection on the thermostat and the transformer.
--
Seth Goodman

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Seth Goodman wrote:

Thanks Seth and all. I see that my assumption that the existing two wire thermost is just a switch is correct and that which way the red and white wires are connected won't make a difference.
If I do run a new thermostat wire, I guess I'll use 3-wire conduit just in case later on I want to put in a programmable thermostat that is powered by the 24 VAC instead of batteries.
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BetaB4 wrote:

If you want to run new wires, run at least 3 pairs. Then you can cover multi stage heating/cooling in case. I am using a wireless programmable 'stat for heating/cooling. If you don't use battery, you can lose clock setting when power fails. Not a good thing to happen. Battery lasts over a year and it keeps clock setting. Also it tracks DST automatically.
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On a heat only system, it doesn't matter. It's just a simple switch.
--
Christopher A. Young
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Correct
Yes, but why would you? Seems like a lot of work for no good reason.
But, if I later change to a

No, and you should get a Honeywell programmable before next heating season. Sets back and night and you have it start warming the house about 15 minutes before you get up in the AM. About $45
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