Under Preferences -> Display -> Formatting click on 'Advanced'. Under 'Font Control' uncheck 'Allow messages to use other fonts'.

I've checked and unchecked everything I can think of, and it doesn't seem to help. Unless it's just that incoming messages are HTML but that doesn't seem to be the case, and it also seems like there was a big change in this behavior as soon as I updated to 31.3.

I've seen no change in fonts behaviour on any of my three installations of TB.

Have you set the required font for all appropriate encodings and fonts?

See the end part of this page:

http://www.ramsden.org.uk/9_Type_sizes.html

from "The fonts used to display messages on your screen are set here:"

Ah, I think I see what happened. When I updated to 31.3 all of my font settings under Preferences were lost. I had to try to remember what I had set everything to. Eventually I got everything right, but only under the Western encoding. I didn't realize I had to set other encodings too. When I set the correct fonts in the Unicode encoding, things start to look a lot better.

I believe that Thunderbird regularly "forgets" randomly-selected settings during upgrades, leading to unexpected changes in its behaviour. If this is a security setting or port number then it breaks the connectivity and email just stops. Sometime it forgets that a user wants HTML and sets them to plain text. So I'm not altogether surprised to hear of it forgetting your font settings.

It is counter-intuitive that you have to make essentially the same setting in several different encodings. I think in the bad old days of Windows/MS-DOS code pages, users of Asian languages in particular would have to choose a font that offered their particular script and alphabet. For Westerners using European languages, Windows and ISO character sets were needed but of course pretty much all fonts could display such languages (since English is effectively the default language of the Internet.) I imagine users of Cyrillic would also need to carefully select suitable fonts.

So the adjustability is all there for a good reason, so that any user anywhere can find some way of having his written language displayed correctly. I'm glad to see unicode/utf taking over from all those regionally-based encodings, as it makes the choice of font a cosmetic rather than functional decision.

In your position, I've gone so far as to edit the prefs.js file (in the Thunderbird profile) in a decent text editor, and do a global search and replace for default fonts and sizes, rather than picking through that GUI interface. ;-)

One more thing: it seems that once a message comes in, it gets the font setting that is current at that time. In other words, changing the font setting will not change the appearance of a message that has already been read. Is that correct?

That doesn't sound right. Thunderbird should parse the header, locate and apply the declared charset/encoding directives and then choose whatever font you have specified for that charset/encoding. It shouldn't be making any arbitrary changes of its own accord. If it can't find a valid charset declaration then it should use your selected fallback encoding, which of course may not be appropriate to the message content.

What I can suggest is that if it's displaying a message while you change the settings, the new setting may not "take" immediately. You may have to close and reopen the message to see the new font being applied.