Is that the DEI cooling solutions thermal wrap?
To answer your question, yes this wrapping does decrease under bonnet temperatures and I have had it on previous cars.
What you have to remember is threefold:
1) You have to remove the manifold from the car to install it properly; this may dissuade you
2) In certain tuning circles, some consumers have complained that this wrap has caused premature rusting of the manifold in certain cases. Whether this is due to the grade of steel used I am not sure, but one thing is for certain and that is that if moisture gets trapped between the wrap and the exposed steel, with the great temperatures involved and a lil bit of O2, I could see this as being a potential problem?
3) As with any product, such as the Phantom Grip LSD etc, there are always users that swear by the product and others that avoid it like the plague. I regard exhaust wraps as one of those products. Some have reported premature manifold wear issues, but I call BS on that if the manifold/exhaust was properly manufactured in the first place. One BIG thing to bear in mind is that practically no vendor will stand behind the warranty on their product if you heat wrap it because you are exposing the metals to temperatues that are outside of their intended tolerance range.
With all that is said and done, it does have it's benefits. I reckon that the weighting is 50/50 risk on this one. If you wrap the manifold not only will you see reduced under bonnet temperatures, but you will also benefit from an increase in performance since ideally one wants to retain as much heat in the exhaust system as possible to aid rapid outflow. It's a tried and tested method on other cars, but I'm not sure how significant the effects would be for the MINI.
It's your call man
BTW, the wrap is only like 35 quid Inc VAT so it's not a huge outlay, but you may want to think it through a little further before using it.
Cheers,
Henry