I don't like using a regex as my only determination that I've gotten a number from the user. I'd rather let Perl tell me with 'Scalar::Util::looks_like_number'. It's more reliable. In that case, you're mostly interested in ascertaining whether you're looking at Fahrenheit or Celsius, and whether the input came in an expected format. This will do just that.

use strict;
use warnings;
use Scalar::Util qw( looks_like_number );

# .....

if( $temp =~ m/^([0-9.+-]+)\s*([cf])/i and looks_like_number( $1 ) ) {
    my( $number, $system ) = ( $1, lc $2 );
    # Do whatever you want here; 
    # $number contains the temp, 
    # and $system contains 'c' or 'f'.
}
else {
    die "Invalid number format.";
}
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You'll notice the regex isn't too particular about what constitutes a number. It allows characters that are reasonable for a number to contain, but doesn't bother with whether the number makes sense. That's the job of "looks_like_number()". That tells us whether Perl thinks it can use the input as a number. We're using the regex just for capturing of the chunks of the input that we think should have a number, and a measurement system.