If you look in the furnace, you should find that the wires go to R and W, which is where they should be hooked up to in the new thermostat.

Pro tip: if you hook the wires up before attaching the stat to the wall, you'll have an easier time and do a neater job.

Is it possible for you to pull new wire? A few nicer aspects of having a modern thermostat (assuming a somewhat modern heat unit) will not be available with only two wires, even if you can get it to work. My wire run was pretty easy so this is what I did. I love to run the fan alone, but that was not possible until I replaced the old wires.

There’s one option I haven’t seen below and I realize you already bought the thermostat… BUT! There are some really nice wireless thermostats that don’t require pulling a new wire. What you have REQUIRES pulling a new wire. Thermostats have fairly sensitive electronics and are matched to a graded and measured wire with precisely known resistance. This means that when you turn your thermostat to 70F it will warm the house to 71f…allow up to 3+/- temp. And turn start the furnace at 67F again. If you use the old (most likely solid core 18g copper) wire you will end up a few degrees in either direction or shortening the life of the new thermostat. This isn’t in the instructions and I’m not sure why…maybe Honeywell likes selling new thermostats every few years to the same person? The wiring advice below is good. Do that if you stick with a wired thermostat but the wireless option for about $180 is going to be trouble free and only need a recharge on the 9V lithium battery about every 3 years. Well…THAT is my opinion and like bellybuttons…everyone has one.

Fairly sensitive electronics...? Shortening the life of new thermostat...? What are you on about?

That is the ramblings of a madman.

The thermostat determines the temperature swing not the wiring. Most residential stats don't have deadzone adjustment. All a stat does is connect white to red to complete the circuit which starts the heating cycle when it drops below the deadzone temp, and shuts it off after the satisfied (set) temp.

In no way would you want a 1 degree swing, generally you want only 4 to 5 cycles per hour on heating. Short cycling doesn't warm up the heat exchanger and more of your money goes out the vent. My commercial honeywell doesn't allow deadzone adjustment but allows cycle limiting and learns what it needs based on the run times and temps.

Good news, these are facts unlike your unfounded nonsense.

Yup, just use R and W on new thermostat but you will need to power thermostat with batteries and configure for heat only, gas furnace option for fan control

This is nonsense. 2 wire thermostats turn the heater on or off. There is no analog signal for temperature.

Appears to be heating only thermostat. Go R to W on new board (E will land on W).

There's nothing intrinsic to the wire that has anything to do with temperature control. Thermostats are just on/off dry contact switches that turn on/off parts of the heating/cooling system depending on some internal temperature measuring device, like bimetallic strips in mechanical stats or thermistors in digital ones. You can even do this manually by shorting wires.

He has no idea what he's talking about. Jesus.

Please don't listen to this person, they are completely clueless. Wire is wire when it comes to thermostats. HVAC tech here.

You will need to run a third wire (a constant). It’s pretty common when upgrading to a fancier thermostat. There should be a spot on your furnace to attach it. If pulling a new wire is doable, it’s a pretty easy job.

Your wires don’t look to be in good shape. If you can pull them out of the wall more, cutting and stripping them back further would be a good idea. If you can’t I would replace the wires.

Exactly. It’s a switch. It’s either open or closed; on or off.

Wire resistance what? You understand that wire resistance is going to change based on not only gauge but length, right? Thermostats work the same whether they’re 2’ from the furnace or 200’ from the furnace, both with drastically different wire resistance.

I would definitely look into pulling a new wire, and I’d run at least a 5 wire, if not 7, to allow for future upgrades.

It sounds like you are trying to upgrade an old 2-wire thermostat to a digital one. Unfortunately, it is not always straightforward to determine which connections to use when wiring a new thermostat. It is important to double check that the wiring is correct before connecting the new thermostat. It is highly recommended that you consult a qualified HVAC technician to ensure that the wiring is done correctly. Additionally, they will be able to advise you on the best type of thermostat to use for your gas furnace.

If it were me, now in hindsight, I'd get a new 5-wire to run. I spent hours trying to get a new thermostat working on an old 3 wire setup and gave up on that; was having too much issue trying to bridge pins and stuff. Once the new 5 wire cord arrived I taped it up and pulled it through, connected it to furnace board & thermostat and it was a 20 minute ordeal.