Problems installing Python on server

[Yansky]

I asked my hosting company if they would upgrade Python on my server
to the latest version. They responded with:

"Sorry no. We tend to stick with what comes packaged with the unix
distribution to ease maintenance issues.

There is nothing stopping you from running your own version of python
from within your own account. Download the source and compile it and
install it into your own space. Adjust the fist line of your python
scripts to reflect the location of YOUR python binary:

#! /home/youraccount/yourlibs/python

and you should be all set."

The build instructions for Python are:
To start building right away (on UNIX): type "./configure" in the
current directory and when it finishes, type "make". This creates an
executable "./python"; to install in usr/local, first do "su root" and
then "make install".

The problem is, I don't have root access to the server so I can't do
the "make install". I have ubuntu on my computer, but from what I
understand I can't compile it on that and upload it because the server
runs Red Had and the ./configure would have made it incompatible
right?

So how can I build Python without root access?