Does Facebook have temporary passwords?

You do indeed have a bit of a dilemma because travel overseas is cool, but when you have to go into an Internet cafe in the middle of nowhere in a third world nation, not only are you going to often end up paying a lot for your connectivity, but you’re right that there’s a good chance that someone — often not even the cafe owner — has installed some spyware or has a hardware keystroke recording device or otherwise can capture your login information.
Then you walk out, they grab the device, log in to your account, change your password, and you’re in the middle of nowhere, unable to fix things while your friends are getting email about you being “stuck in the jungle, needing some extra $$ if they can send some cash to a certain PO box…”
I doubt that’s exactly what Facebook had in mind when it created its temporary password system, but it does have a capability that does exactly what you want, and to use it, all you need is a cellphone with text messaging capabilities.
The critical step you need to do before you’re on the road is to have your cellphone registered in your Facebook account, something that I talk about here: Add a Cellphone to Your Facebook Account.
With that done, here’s how I can get a temporary password from Facebook while on the road, at the local library, or anywhere else I don’t want to enter my regular account password:

As you can see from this iPhone screen capture, I’m texting “OTP” (I imagine that to stand for “obtain temporary password”) to Facebook’s server, 32665 (FBOOK). A few moments later:

That’s my one-time temporary password it’s given me – tgMhztXd – and now when I go to log in to Facebook I enter my account name as always, but use that instead of my regular password:

Twenty minutes after I request the password, whether I use it or not, it expires and no longer works for access to the account. Very useful and something I’d have long since memorized if I were traveling overseas, hitchhiking through Europe, biking the Andes, etc.
Oh, and I should point out that your regular password works too. Now, however, you can be thoughtful and cautious about when you use it versus when you tap into the temporary password capability and keep your main account credentials safe.