Linksys Blue Box Router HOWTO: "There are three ways you can upgrade your Linksys firmware."
The third way is to use tftp. This is how I did it. There is a tftp client included with Red Hat Linux. To upgrade your firmware this way, do the following steps:
Capture a copy of your settings. The firmware upgrade may wipe some of them. Older versions nuked everything back to factory defaults; newer versions preserve your basic settings but clear some advanced ones.
Download a copy of the new firmware. You should find it at Firmware Upgrades for your Linksys Products on the Linksys site. Note that what you get may well be marked "For Windows Users" and be a zip archive. Open it in a scratch directory, because it will rudely create several Windows files wherever you unpack it. The file you need will be called CODE.BIN.
Disable the router password Note that every attempt I made to do this with Mozilla failed (both under 1.38 and 1.44). Konqueror worked fine. Go to the Password tab, backspace over both sets of asterisks until both the Password and Confirm fields are blank, and click Apply.
Cross your fingers and load the firmware The command session you want will to see will look something like this, with your router's IP address substituted for 192.168.1.1:
tftp> put code.bin
Sent 386048 bytes in 10.3 seconds
Don't panic if the client hangs for a bit before returning and do not abort the transfer. The command is writing to firmware, and the Linksys hasn't got much of a brain. Wait for it to finish.
Re-enable your router password and other settings. You'll be able to tell the upgrade worked because the firmware version number has changed.