You can find it from this link: https://www.mozilla.org/en-US/firefox/organizations/all and also from here: https://ist.mit.edu/firefox/ESR/windows

Thank you Azharul you for the prompt post. Unfortunately, the only things I can see on the Mozilla Site only gives ESR 45 or ESR 38. (I'm at work, I'm not sure if my network will allow me to download from the alternate site.)

What outdated application is insisting on using a old version of Firefox like 31?

Since you are on Windows, there is a portable Firefox option as it is self contained and will not affect your Firefox 46.0.1 install or Profile being used with it. It can even be run off a usb flash drive.

copy+paste below in Location (address) bar. The English US is at bottom of list. https://sourceforge.net/projects/portableapps/files/Mozilla%20Firefox%2C%20Portable%20Ed./Mozilla%20Firefox%20ESR%2C%20Portable%20Edition%2031.7.0/

The portable Firefox option is safe as it has existed since Firefox 0.8 version (Yes people Firefox had Releases before the 1.0 version) and has been safe since.