My LC III has a Sanyo Pico Ace 15 60x60x15mm fan, with two wires (1 blue, 1 red) going into a 3 pin connector. Most replacement fans you find will be 60x60x20, so they won't fit correctly.
Well, one way of solving this is to install a chipset heatsink, one that isn't too tall so that it fits in the case. They can be mounted to the chip using 3M thermal adhesive tape. This creates a bonding between the chip and the heatsink, sort of an alternative to thermal paste/grease.