So far the only way I've found to properly insert ˚C is to
\usepackage{textcomp}
...
{\textcelsius} % Note this won't work in math mode. No different spacing is needed around this.
_____________
{\celsius} % Does not work.
\celsius % Does not work, even in math mode.
\textcelsius % Does not work.
I had previously found an online forum that suggested using $^{\circ}$C every time, but that's tedious, ONLY works in math mode, and had caused some errors.