The cover is missing from this thermostat, so I don't what brand or model it is and I don't have the manual for it. 
What brand of thermostat is this
thermostat
thermostat
The cover is missing from this thermostat, so I don't what brand or model it is and I don't have the manual for it.
Best Answer
Most residential thermostats are designed to be easily removed on one of two ways:
The entire device slides up ~ 1/2" and then pulls off the mounting screws
The front pulls forward, possibly with a plastic tab or two on top or bottom pried open with a flat screwdriver, revealing a back panel screwed into wall and containing the connections to the wires going to the furnace & air conditioning.
Either way, once you have it off the wall it is usually easy to find manufacturer/model information.