You could make use of the “piped \input” feature. For example, this is a MWE that inputs from the standard output of a cat command: the same idea can be applied to other commands, and, in principle, also to wget:
\begin{filecontents}{myTempFile.tex}
\section{A test}
This is a test.\par
\end{filecontents}
\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\begin{document}
\input{|"cat myTempFile.tex"}
\end{document}
Of course, for this example I have generated the temporary file by means of a filecontents environment.
Edit
By way of example, let us \input from the standard output of the date command as well:
\begin{filecontents}{myTempFile.tex}
\section{A test}
This is a test.\par
\end{filecontents}
\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\begin{document}
\input{|"cat myTempFile.tex"}
\input{|date}
\end{document}
Here is the result:

Addition
Re-reading this answer, that I had posted more than a year ago, I realized that I had never completed it as I intended to. Just to convince yourself that the answer is “Yes, it is possible to input a file from the web”, try compiling a source file containing just the following, single line:
\input{|"curl --stderr /dev/null http://www.math.unipd.it/\string~mezzetti/Gustavo/Ludic/CDP/presentazione.tex"}
This example uses curl, but it is easy to adapt it to use wget instead. Remember that you have to enable the “full shell escape” feature, in order for this to work.
wgetfrom your LaTeX call, download the file, rename it and compile it. – Johannes_B Jun 10 '15 at 11:51