hmm lets break it down a little,
how does your thermostat work, are you reading values through the arduino on your computer or does the computer directly interface with it?
if the first, you feed the value through to your display after formatting it correctly, e.g. change a reading of x volts to x volts into 0-45 degrees,
this can be accomplished by one of the many libraries out there for arduino, most of them go well beyond what pins to use but reccomend models
lcd vs led, that comes down to how you plan to use the display, an lcd draws far less current, and you can generally fit more information onto it for a given size, but generally the driver will add a few dollars to your design, while 7 segments have excellent readability even over some meters, but can really suck down some current, e.g. 5mA per segment, but is very cheap and easy to drive,
post a scheamtic or some code or even just some more info otherwise i am left with mainly assumptions