Mac OS X - where to find Chrome and Firefox temporary files?

Firefox stores its files in /Users/username/Library/Caches/Firefox/.

Chrome stores its files in /Users/username/Library/Caches/Google/Chrome/ and (very short-term) in /private/var/folders/.

You can see these paths when you run either of the following:

sudo fs_usage -f pathname Google\ Chrome
sudo fs_usage -f pathname firefox-bin

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If you just want to download FLV files off a video sharing site, I suggest using a browser plugin, or Safari's Web Inspector with resource tracking.