Just stack the subcaption text under the subfigure. You can change the fontsize of the subcaptions just by changing the \footnotesize to the desired size. The gap between figure and caption is controlled by the optional argument to \stackunder and is, in this example, set to 5pt (the default is 3pt).
Note that the subcaptions in this technique, will not automatically word-wrap. In your case, there was no need for wrapping, since they were short labels. If wrapping were needed, the last argument to \stackunder could be a \parbox.
I further assumed, that since you wished to remove the (a), (b), that you had no desire to separately reference the individual subfigures. You can still reference the overall figure with \ref{}.
\documentclass{article}
\usepackage{stackengine}
\usepackage[demo]{graphicx}
\begin{document}
\begin{figure}
\footnotesize
\stackunder[5pt]{\includegraphics[width=2in,height=.7in]{fileA}}{MRI-CGCM3}%
\hspace{1cm}%
\stackunder[5pt]{\includegraphics[width=2in,height=.7in]{fileB}}{NorESM1-M}
\caption{November to April}
\end{figure}
\end{document}

\caption*, labels cannot be used anymore on the subfigures. – Derlin Jan 02 '19 at 23:37