If this is the old type (slow reacting) bi-metallic strip temperature
gauge, then a short-circuit of the wire between the sender and the gauge
to 0V (car body) will cause it to read high.  Try disconnecting the wire
at the sender and the gauge should drop to read minimum.  If there is a
s/c of the gauge to 0V then it will still read high.
(I suppose it reads low with the ignition switched off?)

Well I did send a post a few days ago regarding this message/thread but
again it didn't send for some reason via Outlook Express?  Anyway what
year Mini do you have?  Does it have the Clubman style clocks in front
of you?  If it's a post 1985 model, it generally has Nippon Seiki
Instruments instead of the trusty and better (I think) Smiths
Instruments and the Nippon's don't have a voltage stabiliser behind the
clocks as their all electronic unfortunately.

But yes check for shorting somewhere too!