Cooling in a F1 car is the same as cooling in a normal road car. Water is pump through cooling ducts in the engine and absorbs heat. The water then passes through an air cooled radiator where it rejects its heat to atmosphere. The difference is that F1 radiators have no fan and are reliant on forward motion of the car to generate cooling air flow over the radaitors. The pressure in the cooling system is limited by a relief valve set to 3.75 bar gauge . This limits the temperature of the water coolant to about 150 deg Celsius or else it will boil off.
The water temperature will be monitored at several places by thermocouples, or some other temperature sensor with very thermal inertia and quick response time. As best I know there is no attempt to regulate the coolant temperature beyond limiting its maximum pressure.
The cooling system of an F1 car is a very complex and subtle design problem. As a rule of thumb, roughly 30% of the thermal energy produced by the engine's combustion ends up being rejected through the cooling system. If the engine is producing 900 hp, the cooling system must transfer 11,453 Btu/min to the surrounding airflow.
Cooling system design, like everything else on a race car, is an exercise in compromise. To reject lots of heat, you need a large heat exchanger. However, a large heat exchanger is heavy and causes lots of aerodynamic drag. To maximize the efficiency of the heat exchanger, and thus minimize it's size, weight and drag losses, you want the deltaT between the coolant and incoming airflow to be as great as possible. Of course, as ReubenG points out in his previous post, these variables are limited by the rules.
Another thing to consider is, as the cooling air passes across the heat exchanger, it picks up thermal energy and thus exits the cooling ducts at a higher velocity than it entered. If properly designed, a cooling duct can provide a net gain in downforce or forward thrust, relative to it's intake drag losses.
There are also other ways that F1 engines use cooling. A typical F1 engine passes significant amounts of fuel through it's intake. As this fuel mixes with the intake air and evaporates, it pulls heat from the intake charge (this characteristic is typically referred to as latent heat of evaporation). If you look at the fuel injector location on most F1 engines, you will see that they are located as far upstream in the inlet runner as possible. The latent heat effect can produce a significant increase in intake charge density and a lowering of temperature, thus increasing engine power.
Of course, as far as fuel injector location is concerned, the ultimate location is directly in the combustion chamber, like Audi's ALMS car GDI system. Of the total mass flow through the intake system, about 6 percent is fuel. If you inject fuel directly into the cylinder, then you can get roughly a 6 percent increase in air mass flow through the intake ports. On a 900 hp F1 engine, that's an additional 54 hp.
