Thermostat valve is device to bring engine up-to operating temperature as quickly as possible after cold start so you don't consume extra fuel and hurt the environment
Automatic fan system on the other hand would stop your car engine from overheating by having a temperature switch turn on radiator fan at certain temperature.
Ideally both these systems should be working simultaneous in tandem to keep your car engine operating at optimal temperature.
If you remove the thermostat or turn the fan on constantly (direct) it will make the engine run colder which can hurt the fuel economy