For milder states of tune, use the later Mini radiator or Cooper 'S' item. As things start to get wilder look into the following:-
Four blade fan (noisier, but more efficient).
High capacity water pump. You may like to file the inside of the alloy outlet pipe on the pump (i.e. where the bottom radiator hose slides over) to 'gas flow' the coolant passage from pump to pipe. Don't go mad. just take a small amount off around the opening.
Electrical fan - OK, but on a Mini you need to retain the original fan as well.
Larger capacity radiator. The done thing used to be to fit a radiator from the Austin/Morris 1100/1300 Saloon range. Unless you modified mounting brackets etc. a small bonnet bulge was needed. Today you can choose from a Mini spares outlet a 4 core radiator.
If cooling really is a problem the next steps are to bypass the heater unit, diverting the water to a small auxiliary radiator behind the grille. Or you could fit bonnet pins in place of the hinges and by using spacers 'jack up' the rear of the bonnet to allow air to escape.
But in truth, most overheating problems may be traced to the following:
1. Sticking/incorrect/missing thermostat. If you must remove the thermostat, fit a blanking sleeve and block off the bypass on the water pump.
2. Incorrect/damaged radiator cap.
3. Blocked waterways in block/head/radiator (reverse flush out).
4. Too high concentration of antifreeze (too low will cause the block etc. to rust - thus causing point '3' above).
5. Water leaks.
6. Inefficient water pump.
7. Incorrect ignition timing/fuel mixture.
8. Blown head gasket.
9. Broken/Incorrectly tightened fan belt.
10. Too much stuff in front of the grille ñ spotlights, badges etc.
Apart from the faults with brakes and engines etc. those are the main causes of overheating.
Engine Mounts - aligning and bolting up;
One of the most-hated Mini jobs is to line up the engine mounts with the mounting holes in the front subframe and installing the bolts when installing the engine in the car. Some tips:
Find someone with small hands to help you.
To align the mounting holes, keep some upwards pressure on the engine via the hoist/winch you are using to drop the engine in. Rock the engine from side to side to get the holes nearly lined up. When they are close, use a plastic-insulated screwdriver through the part of the mounting hole that is visible, to move the mount around until it lines up.
If you can get one bolt installed (but not tightened up), lining up the remaining three holes is much easier. Each time you get one hole to line up, install a bolt in it.
To get the bolts through the mounts, wrap thin wire (e.g. welding rod) around the thread of the bolt and manoeuver the bolt into place by remote control using the wire. Put a nut on it and pull on the wire - it should unwrap leaving the bolt in place.
Engine mounts with captive nuts are available that do not require the bolts to be installed from the subframe sides, making the whole task a lot easier.