Cold start and temperature gauge reads hot?

So, it's cold today.  -6 F and with windchill it is -21 F.  I started my car today no prob
and it was revving high to warm itself up.  Then the temp gauge leaped from cold to hot,
and I panicked and shut the car off (the car was running for probably a minute).  I'm
thinking it was just the super cold temperature messing with the sensor as my phone
has been left in the cold but battery diagnostics read it as "overheat," but I know more
about computers and phones than I know about cars (and I can feel the real
temperature of a phone easier than an engine), so I played it safe in case I was wrong.  

So, why did the gauge do that?  Is it something I should be concerned about or would it
have fixed itself if the engine were allowed to run longer?