Only one bit of advice:
When you remove the thermostat from the wall, make sure you have some masking tape or a clothes pin or binder clip or something to secure the wires so gravity doesn't pull them back into the wall cavity. You will be unhappy if you lose the wires in the wall. This potential problem is less likely if the wires are stapled to a stud near the hole, but you never know how your house was constructed. Don't ask how I know about this.
Installing a new thermostat is easy. Just pay attention to the labels (if any) on the screws of the old thermostat and what color wires were connected to them. Then wire the new one the same way.
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