I am replacing an old Honeywell thermostat. Heat is a natural gas furnace with hot water baseboard heating.

I have 3 wires: red, white, blue.

Question: I cannot find the proper thermostat. What type of thermostat do I need? Most store brands seem to be tailored for 2 or >3 wire arrangement.

Specifically, where does the blue wire go? Without it, the zone flow valve does not close.

If I was to guess, I would put red on R, and blue and white on W.
If old thermostat still works, I would verify switching on old thermostat with meter.
If fan is able to run with out heat, then blue wire may go to G.

Mj

You state furance than baseboard.. I assume it is hotwater boiler..
Where are the wires going on the old thermo?
.. red blue white.. to what terminal.. some older ones used numbers 4, 5, 6 instead of rh, a, w etc..
If this is baseboard hotwater is it multiple zone?? usually is with 3 wire..

What you need to do is go to the furnace and identify what the wires do. Usually red is from one side of the control transformer, and the thermostat switches it to white on demand for heat and the white activates the furnace. Blue may start the pump or something.

The zone flow control valve has 6 terminals on the back, numbered 1-6.

Terminals 1,2 and 3: power the valve and connect to the pump

Terminals 4,5 and 6 connect to the thermostat ( the 3 wire arrangement).
Terminal 5 powers the valve.
Terminal 4 OPENS the valve.
Terminal 6 CLOSES the valve.

This is where I'm having trouble. The blue wire (extra wire) lands on terminal 6 on the valve, and is needed to close the valve. However, on the thermostat end, I have no idea where to land the blue wire. Every wiring configuration I've tried has the same result... the heat turns on normally, but never turns off. In other words, I'm not putting the blue wire in the right place.

I'm beginning to think I need a special type of thermostat. The thermostats I've tried appear to only require giving the valve one demand. (fails closed, and power to open. Or vice versa). The common thermostats do not seem to be wired for a valve which requires both a signal to open and a signal to close.

Apparently the old thermostat used a double throw switch to close the valve. What you can do is use a double throw relay. Connect W and the transformer common to the coil. Connect red to the relay common. Connect #5 to the NOC, and #6 to the NCC.

Try this config

Zone thermo
R or 5 to terminal 'rh'
W or 4 to terminal 'w'
Y or b or 6 to terminal 'a'
The terminal specified would be on the new thermostat.. just went through this at my parents, they have a 40 year old 3 zone valve boiler had old white and rodgers thermos exchanged them for rite-temp check this website
The RiteTemp Support Site - Zoned System Guide

If this is a White Rodgers 3 wire zone valve you will need a compatible thermostat for the system to work correctly.

The hot water heat at my church works just fine with the zone valves controlled by relays wired up just as I said. It is going to be cheaper and easier to find a relay to make the thermostat you have work, than to find a programmable thermostat that will provide a valve close signal.