How to insert degree Celsius symbol in node text in pgfplots/tikz?

Here are two other options:

$44.9^\circ$C
\SI{44.9}{\celsius} % \usepackage{siunitx}

I prefer the second one (if siunitx is used anyway).

Just use \textdegree{}C

Attention, you need to say \usepackage{textcomp} in your document's preamble.

Most is said already, but it's worth mentioning, that $^\circ$ and \textdegree{} yield different symbols:

So either

\usepackage{textcomp}
44.9 \textcelsius{}

or

\usepackage{siunitx}
\SI{44.9}{\celsius}

or if the exact typesetting is not important, this works as well:

$44.9\, ^\circ$C

If the curly brackets are omitted after \textdegree{} the space behind is ignored. \textdegree\ does the same job.