Kevin ignore that guys posts, all of his postings have made no sense or do not relate to the posting. They all have that link attached trying to flog his stuff which is his only purpose for posting i am suprised Don/Dennis has not evicted him yet.

I knew Kevin would post with the oil recommendation.  I second the suggestion and method. 

However, if you cannot find the oil he uses or if you are lubing a rack still on the car, I have had no problems with standard 90W gear oil and filling each boot with a bit of oil as called for in the early Haynes Mini manual. 

Um... mate, these are Mini racks, (made 1959-2000) not MINI (BINI) ones. No power assistance on these puppies!

It sounds as though the system isn't pumping the Fluid around steering system and as a result it is just feeding it back to reservoir thus heat is being generated by pumping action but as it isn't being used to feed steering rack you will notice the heavy drag effect on steering wheel due to no hydraulic assistance.
something has gone wrong here probably with the pump itself or system is blocked.

Steering Rack

They sell gear oil at a coffee shop? That might explain why I don't like the taste of coffee.

When I did my Mk3 Mini I used 90-140 gear oil that I use in my Dodge Cummins Turbo Diesel, about 4 ounces.  If your going to Cars and Coffee at MINI of Tempe tomorrow you can stop by and pick up some.

Original rack lube was 140 gear oil.

Yes they put lithium grease in them from about 1980 on (to avoid leaks, it was BL's idea not the rack maker's) but it doesn't give lasting lubrication. The rack cuts a track thru it when it's dried out a bit, and then no lube. Then the bearings rust, the felt bush wears, and the preload saddle thingy too. Maybe they could have used proper semi-fluid `rack grease', but they never did.

I rebuild Cam Gears/TRW AYA6001 Mk1 Australian racks, my lube of choice is Castrol 85/140LSX. My rack boots don't leak, I seal them onto the rack body with Loctite 515 master gasket then cinch the zip ties up. Ditto a 515 smear on the preload shims. No leaks.

[edit] typo

[edit 2] To fill with oil I stand it vertical, pinion end upwards. The Oz racks take 200mL. It takes a while to fill them as the thick oil needs to get below the bush and displace the air. Don't be hasty...
Then fit the other boot as described.

What kind of grease? Sorry...I have never done this, so get to basics.

Gear oil is specified for MkI/II (Cherry flavor?). I believe grease became the OEM material at MkIII. If you boots are good the oil doesn't leak out. There are some practicioners who swear by oil.

Grease!!!

Oil will just piddle out of the rack boots.