When the engine is cold the themostat is closed, which forces outlet coolant back into the engine through one or more bypass circuits without going through the radiator. After a cold start the coolant in the radiator basically sits there without circulating, and it will remain near ambient temperature regardless of air flow or lack of air flow through the radiator.

Once the themostat begins to open, coolant flows into the radiator forcing the cold and cooled coolant into the engine. The thermostat doesn't control coolant flow through the engine. It controls coolant flow through the RADIATOR!

Fans are needed primarily at no or low road speed. A fan clutch allows the use of a large fan that flows lots of air at idle and low revs without excess noise or parasitic power loss at high revs.

Duke