If you have your own mail server and view your mail locally on a client like thunderbird, you can’t really view your mail on any machine in which you don’t want to be installing an email client on or one that isn’t yours. Are there any self-hosted webmail options in which you can log into your email on any machine without using a 3rd party service?
The usual ones are RoundCube and SnappyMail (which is a fork of deprecated RainLoop). I’m hosting SnappyMail to access my Dovecot when no other mail client is handy.