OK guys I'll concede it can happen, but I've never seen it in nearly 50 years of Mini-ing.
Only slightly off topic-
My son had a S/H Audi A4, 1.8L turbo- somehow he once managed to get it so hot the AUDI logo melted off the top. Was traded soon after on a new Hyundai i30.

Sorry Kevin i have also worked on two 1275 Mini's with melted oil caps from overheating, both are still running fine with good power but the second one did need a replacement head due to 3 cracks and two valve seats that let go.

I was driving from Regina to Saskatoon one January evening in extreme cold when the water pump failed about 20 miles from Saskatoon.  My sister and my very young neice were with me.

Again, this was extremely cold; -35C or colder.  I added coolant to the 998, and it poured straight out the nose of the water pump.  I removed the cardboard winterfront from behind the grille and drove the car.  I got home without a lot of drama.  A couple of days later I changed the water pump in just over a half hour.  It was still really cold out so there was great motivation to work quickly.  That incident did not melt anything, though it probably didn't do the rings any good.

Yup. An overheated engine can melt the bottom of the cap. I checked a 998 out for someone that had very low compreession. After pulling the valve cover, I noticed a black, plastic-like substance molded onto the section of the rockers and shaft right below the cap. Then I turned the valve cover over to discover the bottom of the cap had melted off.

The owner admitted to driving the car home a 1/2 hour drive after she noticed the temperature needle pegged at H. She said she wondered why the car wasn't running very well by the time she got it home.

Instead of pulling over and calling AAA to pay for a tow home, she got to pay for a rebuilt engine.

That's why I like LeMons: Doing things others say can't be done!

Kevin, who has the distinction of schooling me every now and again:  You are getting schooled:

My sister completely overheated the 1300 in my dad's daily driver mini.  The red engine paint on the head and top of the block turned brown.  The cap totally melted into the rocker gear.  Summer of 1986.  Engine is now a 70 000+ mile 1380.

I think the cap in the photo above fell onto the header.

No way the engine can get hot enough to melt that cap in situ, somebody has dropped it onto the headers I bet.

BTW it pays to keep Mini engines topped up to the full mark. If it gets below min mark, you can get oil starvation on RH turns (due to the dumb place the pickup strainer is in). 
That's why they make center oil pickups as an aftermarket part.

My 1981 mini with 998cc motor has a slight oil leak. Before I take it out for a drive, I always make sure the oil level is between min and max on the dipstick. For the past 2 drives, I didn't check the oil Level. Once I did, I noticed it was sitting a half inch below the minimum line. After opening the oil cap to pour a little under a quart of 20w50 oil to have it sit right below the max line, I noticed the inside of the oil cap was melted [picture below]. Kind of hard to see but almost looks like a perfectly smooth cylinder carved it out as if someone let it sit on a hot exhaust pipe. 

Whether this was here from the previous owner, or from me because my oil level was low, I'm not sure. Is there anything reason the engine that can get hot enough to warp the oil cap? I've always kept an eye in the water tempture gauge and its never come close to over heating.