You trust computers you control? That's so cute.

http://cm.bell-labs.com/who/ken/trust.html

True, but you can only go so far down the rabbit hole until you think you've done enough due diligence to remove as much risk as you feel comfortable with.

You couldn't use a USB key instead?

Sure I could. Not denying that there are other ways to get access to the files I need, just that this has become a part of my workflow that two-factor auth disrupts.

I think having a second gmail address just for emailin yourself files for public computers might work for you. Keep your personal email safe, and forward what you need to the other address. It's a good compromise.

Don't underestimate how vulnerable you are when your email gets hacked - virtually every service you use can be accessed by the forgotten password mechanism when your email is breached. I'm pretty lazy and have procrastinated for a long time, but with the recent attacks and realizing what a mess I could face if hacked I finally implemented two factor auth and I have no regrets yet.

The problem of having to type in your password on an unsecured machine still exists.

To access files in this situation, a better approach would have been to upload the file to a webserver. You can then safely download it from the library computer without anything being compromised.

You'd only have to type in the password for an email you don't care about from the unsecured computer, as long as you knew ahead of time to forward the things you needed to print from the library computer. The web server method seems a little less secure since rather than having your files behind a non-two factor email account, they're publicly available. How is that better?