cool air intake

Engine power output depends on the amount of air that passes through per unit time. The fuel injection system senses the mass flow and schedules fuel in proportion. For a given volume, cold air has more mass than hot air, so drawing in cool air will allow more fuel/air mixture to be burnt than with warm air, and therefore more power can be generated at a given engine speed. A smaller throttle opening can therefore be used to maintain a given road speed, and because engine efficiency is related to the difference between intake and combustion temperature, there will also be a slight improvement in fuel consumption.
The density of air is proportional to its absolute temperature, so an estimate can be made of the possible increase in mass flow due to a reduction in intake temperature. A simple experiment of putting an air temperature sensor in the existing intake showed figures of between 10degC and as much as 25°C above ambient under different driving conditions. Taking the worst case, 25deg is 318degK at an ambient temperature of 20deg(293degK), the ratio is 318/293=1.085 or 8.5% greater density. An MGF 1.8i with 118bhp won't deliver that at the wheels, but whatever does arrive there could now be that 8.5% greater. That makes it a worthwhile aim if it can be reasonably easily achieved.
The device I used was a little battery-operated air temperature sensor with a remote thermistor which I can't guarantee would have been measuring true air temperature. It could well have been affected by radiant heat, but nevertheless showed some pretty high values.

There has been a fair bit of discussion about this over the years, and Rob Bell's website has some interesting stuff. Go to http://www.mgf.ultimatemg.com/ and follow the links to technical stuff and intakes to find a lot of good reading matter.
I've been trying to decide the most cost-effective way of getting a good improvement for a while, and finally arrived at the following system. All I've done is bypass the existing intake duct system ahead of the filter box, and run a duct to the nearside vent. Nothing fancy, but it means that the air entering the duct is at least at ambient. The wider the throttle the faster the air's going through, so it has less time to warm up, so it was potentially going to be reasonably effective.