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.
During flight the pilot must keep an eye out on engine temperatures so that they are within operating limits, this page explains some tips on how to keep the engine cool.
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.
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).
You will need to open these during high power flight or when taxiing on the ground when air flow is at its lowest. Just remember: use them when the engine creates a lot of heat and cooling air speed is low.
During the preflight check, make sure that any coolant or oil radiator is clean and not obstructed in any way. In winter time some might block part of these radiators trying to keep the engine temperatures within specification.
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.