SquirrelMail
Overview
PHP-based, old, but still good. You can install it on Fedora as squirrelmail.
Setup
You'll need to host your email locally. That means you'll either have to have the email sent to a properly configured sendmail service (or on of the sendmail alternatives), or you'll have to run fetchmail to grab the email and store it locally.
You'll also need to get your local httpd server running SSL. See Apache.
Configuration
I modified /etc/httpd/conf.d/squirrelmail.conf so that the line:
Alias /webmail /usr/share/squirrelmail
reads:
Alias /squirrelmail /usr/share/squirrelmail
This is so that the access URL is http://127.0.0.1/webmail.
Note that it will redirect you to your secure site. Be sure you have mod_ssl installed.