can I install a new thermostat by just turning off the power instead of turining off the circuit breaker?
Yes, but I would 


test the voltage at all the thermostat connections before proceeding.
use an insulated screwdriver.


Some thermostat systems operate at safe low voltages (e.g 24 V) but in some countries, it is common for thermostats to be switching dangerous voltages (e.g. 120 or 240 V) so changing a thermostat needs to be handled with as much care as changing a light switch or lamp fitting.