I thought I wouldn't be able to tell the difference, but when he told me to pause the video to try to guess, I listened to the audio of pouring water again, and thought about "which one sounds like when I pour tea", and that way I could identify the warm/cold water. Interesting!

I noticed the sound when making hot chocolate for my child. I figured there are a number of things at play... the leidenfrost effect when the water hits the much hotter edge above the waterline in a kettle(not in this video), the air over the hot water being more humid (and thus lighter), the much higher vapor pressure, the difference in surface tension, the dissolving of the hot chocolate powder, etc.

Viscosity isn't something I considered... but it makes sense.