If the vehicles thermostat is on top of the engine or near the top of the engine which it normally is then yes you need to drain some of the coolant out.
You don't need to drain all the coolant out of the engine and radiator though and you only need to drain part of the coolant out and just enough coolant to drain it so the coolant level is below the level of the thermostat housing.
Wait for the engine to cool down though before draining the coolant to avoid getting burned by the hot coolant.
Then use the drain valve on the radiator to drain the coolant out into a clean bucket.