Most digital thermostats require a ground (24V common) If you don't
have one the batteries will power it for a few days, then it will die.
Get a mercury non programmable thermostat or run at least a 5-wire
cable and hook up 24V common.

You may be able to get your system to work with a power robbing
thermostat. Those will work without a common. They use the Y & W as a
ground (common) when heat or cool is off, using just a trickle of
current to power the thermostat. Power robbing thermostats usually
don't have back lit displays, as that requires more power than they can
steal.

Stretch