Looking to maximize the under bonnet cooling without visual external implications. Any ideas or tested and trialed outcomes out there?

I had played with raising the rear of the bonnet but it looked bad for a road car.

Why do you need the extra cooling? The standard mini cooling system wass quite good for its time - a clean radiator, clean block, good coolant and a good fan (that's the right way around) will cool almost any mini, even in Australian conditions. So long as your thermostat and water pump are in good order.

I have heard of people using an additional heater core as a 2nd radiator. Some also use an electric cooling fan which is probably better for traffic.

Relocating the radiator to behind the grill is the biggest improvement you can make.
Most turbo minis go this way, not really required for normally aspirated IMHO.

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Too many cars, and too little time.

I don't think Besser means engine cooling, but rather engine bay cooling.
A lot of heat is generated with the exhausts so close to the bulkhead.

He could wrap his exhaust might take some heat away

Yah, the block is around 80 degrees celsius, and the exhaust runs up to 800(ish) degrees, but only at very high load over extended periods. The engine bay is painted, but the temperature doesn't even get high enough to damage the paint.

I'm not sure what you are after in removing the heat, is it better cooling or keeping the bonnet and panel temp down inside the car? Getting heat out of the engine bay is best done then by getting rid of the highest source being the extractors. Have them wrapped in heat wrap, or ceramic coated. It will keep the firewall temperature down as another benefit, and help prevent fuel system vapor lock in summer. The block is also a source, but is stabilized at the thermostat temperature of between 70 and 90 degrees, depending on the one you have fitted, so its not a significant source. engines are very cleverly designed things aren't they!

A thermo fan can draw a larger volume of air through the guard when the car is not moving, but this is dwarfed once the car starts moving above 20 (ish) kph by the positive pressure under the bonnet through the grill.

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SooperDooperMiniCooperExpertEngineering

All garage work involves equal measures of enthusiasm, ingenuity and a fair degree of irresponsibility.

More horsepower = more heat.
So to reduce heat you need less horsepower.

Problem's fixed.

Just a thought about raising the rear of the bonnet.
On a conventional car where the air passes through the radiator becomes hot and then much of it
passes out via the raised rear end of the bonnet. This would be quite effective in quickly removing the hot air rather than stagnating in the engine bay and finally forced under the vehicle.
With a mini, raising the rear of the bonnet would I imagine, reduce the radiators ability to cool when at speed because the fan becomes useless at speed and the radiator now relies on air just rushing through it. Raising the bonnet would reduce the pressure in the engine bay and reduce the volume of air forced through the radiator and possibly only a minor effect on engine bay temp as it still doesn't provide an airflow pass the
exhaust system.
But as you say, the look is probably not suited to a mini. More a tough look for old school Fords and Holdens.

Raising the rear of the bonnet will result in the oil leaks going onto the windscreen instead of under the floor.

I've had extractors Jet-Hot ceramic coated and this really does make a noticeable reduction in the under bonnet heat. They look the biz as well.

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1969 Mk1 Cooper S - "Madge" (the plastic surgeon is calling....)
1970 Mk2 Cooper S - "Vinnie" (Almost there....almost there...)

Is it worth using a sheet of alloy or tin to "block" off the under side of the subframe to seal the engine bay better. Would this help the flow through the radiator and possiably around the engine and past the exhaust if a gap is left under the diff/exhaust area?
You could always cut out the drivers side inner panel and add a extraction/thermo fan there but they may reduce the radiator air flow...

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Respect mine and I'll respect yours.

If it aint broke don't fix it

Raising the rear of the bonnet will not improve engine bay temperature.
The bottom of the windscreen is a positive pressure area and if anything, air would be forced under the raised rear of the bonnet.
For proof that this area is positive pressure, all modern cars have their cabin air inlets there, L34 Toranas and Transams had a reverse scoop the Drew air from the bottom of the windscreen.

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Find a job you love and you will never have to go to work !

Phil you are right for driving , but...
When I ran my Fiat 124 Sport in hillclimbs, I had to pack the rear of the (forward tilting) bonnet up to prevent fuel vaporisation from heat soak whilst waiting in line. Otherwise, it would get off the line, then hiccup....
I don't think a Mini has this problem though, as there's no front mounted radiator filling the engine bay with hot air.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.