The thermostat regulates the MINIMUM operating temp of the engine. It does not regulate the MAXIMUM temp. When a 160 degree t-stat is open, it flows the same amount of coolant as a 195 degree t-stat when it's open. The max temp of the engine is controlled by the size and efficiency of the radiator. Forcing an engine to run cooler than it was designed to will cause poor gas mileage. And other problems...
The mechanical fan has a viscous coupling, commonly called a fan clutch. It allows the fan to slip a lot (run slowly) when the air coming thru the radiator is cool. It engages and speeds up the fan when the air coming thru the radiator is hot. Overheating at low speeds (low air flow conditions) such as stop-and-go traffic is usually caused by a bad fan clutch. Replace. They don't last forever, anyway. Make sure you get the one with the funny little flat coil spring in the front.
And the electric fan comes when (1) the AC is turned on, OR (2) when the coolant gets hot... around 215, I think. You need to get that fan fixed also.
The road goes on forever, the party never ends....