cat command - will it overwrite?

cat ~/temp_minhakey.pub >> ~/.ssh/authorized_keys

appends the contents of ~/temp_minhakey.pub to ~/.ssh/authorized_keys, it does not overwrite it. This is safe.

You might be confused with a single > which overwrites the file. The next command will overwrite your authorized_keys file:

cat somefile > ~/.ssh/authorized_keys

The last part of that command has nothing to do with cat; the >> is a shell redirect that will always append to whatever target file you are specifying. If you used > instead, then it would overwrite the file.

There are several other shell redirects, and you will be more productive on a command line if you learn what they all are and when to use them:

http://www.gnu.org/software/bash/manual/bashref.html#Redirections