OK so it a different motor but on my old 850cc Mini back in 1967 if I drove on the motorway the old two foot long early gear shift not only got hot but when you left the Motorway and tried to change gear it was almost impossible to get it out of top or change gear until it had cooled down - this only took about 5 mins.
You could fry an egg on the drivers floor as well !
My first car was a Mini, 850cc 1971 version, it had the floor mounted long gear lever, guess what gear you are in.... the lever moved 6" side to side when it was in gear....
The later ones had the remote shift and were better.
When I investigated the reason for the "sloppy stick" it was mostly caused by loose mechanical connections, some shims (ie bit of thin metal from an oil can) wrapped under the clamps helped this. Also the fact that there was a grease nipple on the rear of the box where the selector slid through, it never got greased so wore like hell. Bet you didn't know that was there....
My floor never got hot.... it was air conditioned, like many Minis of that era,
if you went through a puddle you lifted your feet out of the way.:lol
The boot floor dropped out on mine through rust and also all of the spare parts I carried. Oversized battery, 2 spare wheels as I was changing over from cross ply to radials, and money was tight.
A spare gallon of petrol because the fuel gauge was broken.
A spare distributor, complete with new points and cap and marked up so it was a straight swap, 2 minute job. A coil, Haynes manual or equivalent.
A heavy tool box, a bypass hose (common failure...) tow rope, jump leads, even AA membership.... Gallon of oil, 1 pint per full tank (5 gallons). Gallon of water.
I think the engine was 850cc but the bore had worn to 1000cc :lol a bit of piston slap.. I guess.
Tried that piston Seal once, added to each cylinder, boy the smoke screen was like James Bonds car for about 10 miles.:doh
Made no difference though....
I was never stranded, broke down every month but I had the spares in the boot.....
It was a good car ......:nenau