The Vintage Mini racing community has about a 'zillion' "cures" for overheating, none of which I am totally in agreement with. Most ideas include auxiliary radiators and such, not a bad idea, just a 'clumsy' idea. I'll tell you what I use on my racing 1963 1380cc Austin Cooper(~135hp @ 7600 rpm with a CR of 13.87:1) that weighs in at 1385 lbs. dry---Also it has NEVER overheated (knock wood) even in a two hour race at Willow Springs where the air temp was ~105f degrees!!!
I use a "Two Core" rad sold by MiniMania, stock replacement with the stock fan shroud. Fan is the 11 bladed yellow plastic fan---I once tried the OEM "tropical" fan and it seemed to work almost as well, but it's metal and heavy. I switched to the "high output" water pump with stock diameter pulleys. I have routed the heater outlet at the back of the cylinder head to the radiator tank via a 3/8" hose (to aid in cooling the #4 exhaust valve). I alternate between a 180f degree thermostat and a "blanking sleeve" to slow the water return to the rad and help prevent pump cavitation.
I use a 19 row (too big for street use) oil cooler with a remote mounted racing oil filter and a 3 qt. oil accumulator for a total oil capacity of 10 qts. (this is in no small way responsible for added cooling capacity). All this works for me, but is obviously not totally suitable for street use.
For my brief time with a street Mini, I used a "four core" radiator (hot setup at the time) that did NOT work all that well---"Two Core" along with the OEM 'tropical fan' was much superior in cooling. I did use a smallish ex-Sprite oil cooler---seemed ok on the streets and freeways of Southern California in the summer where temps in my area are often 110f and more.
When I hear of major overheating problems with Minis (all too often it seems) I first question the quality and condition of the radiator. You cannot use one indefinitely without service to clean out deposits, etc. Properly cared for, many older rads will work "forever" (My 30 Ford rad is still going strong), but many of the newer replacement parts are inferior in quality and construction, thereby limiting their ability to cool sufficiently, IMO. Stick with the basics, quality parts from trusted vendors and you will usually be ok.
Two additionl comments---Always use a fan, the bigger the better, IMO. The side mounted rad needs the fan to get the airflow pointed in the proper direction. It has been proven in racing Minis that a "remote filler tank" in the cooling system will prevent coolant loss and thus prevent overheating from that cause. Mine is mounted on the fender inner panel and is connected to the rad by the standard overflow hose. I use a 7 lb. cap on the rad and a 15 lb. cap on the remote tank. The overflow from the remote tank goes to a one qt. plastic bottle via a small dia plastic tube (no coolant has ever made it that far, at least not yet)!
Some vendors offer aluminium radiators, I haven't tried one yet, but the guys that use them swear by them. Kinda pricey but I want to try one if my situation ever changes. Like I said before, "don't fix it if it ain't broke"!
Rod