Aircraft engines need some form of cooling to avoid damage to the engine. The heat generated by the combustion process is only put to work partially and the rest will warm the engine and must be directed away through some form of cooling system. This will keep the engine within temperature limits as to ensure reliability and long service life.
Most commonly used piston aircraft engines have some sort of air cooling but there are some types that are using a liquid cooling system only or a combination of both, all with their own (dis)advantages. Gas turbine engines use secondary or external air to cool internal engine parts.
The lubrication system is also part of the cooling system, circulation oil will keep the internal parts like bearings and such on a certain temperature within specifications. This page here will concentrate on external engine cooling.
The cooling system is designed to reduce and control the temperature of the engine and in particular the cylinder barrels and heads, which contain the combustion chamber and valves. Other parts like bearings and pistons are usually cooled by recirculating oil with its own (sometimes thermostatically controlled, recommended!) cooler.
If there was no cooling at all the temperatures would rise to such high levels that detonation would be guaranteed with even more internal damage as a result. If left uncontrolled, the metals inside the engine would be red hot and even oil will start to boil and loose its effectiveness. Engine failure is then unavoidable.
Most of the excess heat is lost through the exhaust (this explains why the turbo gets red hot at high power settings) and oil cooler, but some 33 % must be dissipated by some form of cooling, be that air or some form of liquid solution.
Radial engines are a perfect example of air cooling, all cylinders are equally exposed to the airflow and there is an even temperature distribution. But the form of the engine constitutes high drag due to the large frontal area. Inline four, six or eight cylinder aero engines are almost exclusively air cooled, except for the Rotax, Viking and Subaru engines and some aero diesels. It is a good compromise to get a low drag form and there is no weight penalty compared to liquid cooling designs.
Air cooled cylinders have a large number of cooling fins cast around the heads and barrels. This increases the total cooling area, but it can be too effective in winter time or at altitudes above the freezing levels, a winterization kit is then used to control the incoming airflow. To guide the air from the intakes to the engine ducts, baffles and plates are used to maintain a positive air pressure above the engine underneath the top cowling. These items are very important to maintain the correct engine temperatures and an even cooling of all cylinders.
Cool air is taken in at the front of the engine and after cooling the cylinders, the warm (and expanded) air needs to be exhausted. This is done through openings in the lower cowling, sometimes controlled by cowl flaps. These pilot operated flaps are open during high power/ low speed operations (letting more air through during climb and taxi), they will also increase the parasite drag of the aircraft when in the open position. During normal cruise and descent the cowl flaps should be closed.
This type of cooling has a weight penalty but this is offset by the advantage that all cylinders are even in temperature, they cannot be shock cooled during high speed/ low power descends and the coolant can be thermostatically controlled so that the engine is quicker to warm up and remains on a constant operating temperature at all times. Which extends into more reliability, lower fuel consumption and longer engine life, to name but a few advantages.
Modern engines (Rotax, Viking) are all liquid cooled. Indeed, there is more weight and you need to check extra fluid lines and a radiator, but the advantages are there and the system can be very reliable if maintained properly. Personally I never had any problems with the cooling system of, for example, a Rotax.
The propeller spinner is part of the cooling system as it guides the incoming ram air to the intakes, usually to the right and left of the spinner. These intakes are square / rectangle of shape and the more modern ones are round. These have lower drag, thus more effective by reducing the total aircraft drag.
Running the engine with a richer mixture will also lower combustion temperatures and help cool the cylinder head temperatures (CHT). Flying in a high power configuration should therefore be done in a full rich mixture condition unless you need to lean to recover lost power due to high density altitude conditions (temperature, altitude and QNH).
Flying an aircraft without a CHT or any other temperature indication and without cowl flaps requires you to be aware that during long climbs (low airspeed) and high power settings the CHTs could be too high (of course this is no problem with liquid cooling).
Also with extended descends at low power settings the CHTs could become too low resulting in shock cooling (no problem with liquid cooling). During long taxi and idling on the ground (high traffic situation) the CHTs could run a bit high (again, no problem with liquid cooling).
With air cooled engines the CHT gauge becomes very important for monitoring temperatures. Even with the correct mixture setting, when leaning, you will use this instrument in combination with fuel flow gauges, if available. The need to open the cowl flaps can also be followed on the CHT gauge. CHT temperature sensors are normally installed on the 'hottest' cylinder. This will not so much depend on the location (front or back) of the cylinders but on the mixture ratio which is burned in the cylinders. CHTs should therefore be installed and indicated for all cylinders.
With liquid cooling all of the above mentioned problems do not exist. The need remains to monitor the CHT temperatures as this will be the most direct indication of engine health. Liquid cooled engines will usually have an extra coolant temperature gauge, sometimes the CHT is used to indirectly monitor this.