My multimeter came with a thermocouple, but I noticed that the heatshrink tubing says 125 degrees C on it. I think I found the datasheet for the tubing:
www.mantech.co.za/datasheets/products/S901-2_SALIPT.pdf
and the multimeter (not much useful information in there):
www.mastech.com.cn/down/MS8221 series.pdf
I'm worried that the tubing will turn into a smoking mess if I use it for temperatures of 300C or so. The white part of the cable feels like glass fibre or similar so I think that should be OK.
Should I cut the heatshrink off?

 

I'd remove it, for all you know, behind it you'll find a blob of solder connecting the couple to the wire.

 

The heat shrink tubing is trying to keep the fiberglass from unraveling. If you remove it, you should try to think of something that will accomplish that job and survive 300C, like, teflon.

 

Thanks, I got rid of the tubing and wrapped a little iron wire near the end of the fibreglass (I didn't find any solder in there). Just measured my soldering iron at 280C and the fibreglass, or whatever it is, seems fine with that.

 

Good job!
...

 

so funny to me..
400 deg C. rated meter/TC but yet they stick 125deg C UL rated tubing on it.
That "glass fiber sheathing" is probably just nylon string/cord too.

 

Yes, pretty funny. The soldering iron doesn't melt the sheath, so I think it is probably the right stuff.
I'm glad I spotted it, but as it was essentially free with a fairly cheap multimeter, I'm not really bothered.