Converting pgfplots usage to includegraphics (cannot use -shell-escape)

Question

I am uploading a paper to arxiv, which does not allow the use of shell-escape.

Currently my paper uses pgfplots as in the following MWE:

temp.tex
----------------------------
\documentclass{article}
\usepackage{tikz,pgfplots}

\begin{document}

  \begin{figure}
    \begin{tikzpicture}[domain=-2:2]
      \draw plot function{x*x};
    \end{tikzpicture}
  \end{figure}

  \begin{figure}
    \begin{tikzpicture}[domain=0:4]
      \draw plot function{sqrt(x)};
    \end{tikzpicture}
  \end{figure}

\end{document}

When I compile with the following, everything works fine:

pdflatex --shell-escape temp.tex

How can I create the figures and include them in my document without using shell-escape? Ideally, I would run some script to produce fig1.pdf and fig2.pdf, then replace the MWE above with:

\documentclass{article}
\usepackage{graphicx}
\begin{document}
  \begin{figure}
    \includegraphics{fig1}
  \end{figure}
  \begin{figure}
    \includegraphics{fig2}
  \end{figure}
\end{document}

Answer 1

I'm sure there are many possible solutions, but it was relatively easy for me to use the solution linked by samcarter: Script to automate externalizing TikZ graphics

Afterwards, a friend pointed me to the following answer which seems to do the conversion automatically: https://tex.stackexchange.com/a/271475/5097