How to get a copy of an older version of a file in a git repository?

I think that the best solution is to overwrite temporally your file. In your top-level of your repository:

git checkout <sha1> file.tex
cp file.tex directory
git checkout HEAD file.tex

Use git show with absolute repository paths:

workdir$ git show revision:repo/module/package/code.file > code.file.old

or paths relative to the current directory:

package$ git show revision:./code.file > workdir/code.file.old

In contrast to checking out a file, show does not intrinsically change your workspace, you can do anything you like with the output.

Credit to this answer, and of course see full details in the manual.

You can use git cat-file to dump the contents of the file to the standard output and redirect that into your desired destination:

git cat-file -p <sha1>:./file.tex > wherever.tex

The ./ is necessary if you are in a subdirectory of the repository, if you're in the top-level of the repository it may be omitted. Also, that may not work in older versions of git, in which case you'd need to explicitly supply the full path to the file relative to the repository's root.