Trane thermostat replacement
 

I am wanting to replace the slider thermostat with a low cost digital replacement. I dont need the program type or with remote acess. I just want one that will wire up without any modification or having to run an additional wires. I can remove the one i have and install new one, but i just want to match wires up. This is in a Patio Villa. I am just wanting more accuracy in setting the temp.

All thermostats may or may not have these designations. They are the following...
R hot 24V
G blower
Y1 1st stage cooling
Y2 2nd stage cooling
W1 1st stage heat
W2 2nd stage heat
O reversing valve
C common
E emergency heat
You didn't mention if you have a heat pump or natural gas heat. If a heat pump be aware that the O designation can be programmed/wired to either energize or de energize the reversing valve in heat mode. If you have a heat pump it can be tricky if your not familiar with such logic. If you have straight cooling with a natural gas furnace it's a lot easier.

we have gas hot water,,, and there is a gas pipe to the furnace....

you have baseboard hot water in the villages??? only 2 wires for baseboard white and red.............r w very easy

Sounds like you do have gas heat. Simply wire the new thermostat wire for wire to the new one making sure you record the colors.

He meant he has a gas fired water heater, not BB.