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The plastic got pretty hot tbh. I don't bother with a temperature controlled kettle or anything, I usually let it boil, turn off, and give it 20 seconds to cool a little but with this I just poured it straight in to the Hario. Also I boiled more water than needed so I could top up the Hario, I figure the less water in it the quicker it'll cool.
If I end up using slightly too cool water I'm fine with that cos it means I can drink it quicker.
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I normally try to get the water right off the boil for brewing (I recall seeing a video where the slurry temp was measured and it never got about 93-94 even with water right off the boil due to heat loss from the kettle to the cone). Most of my filter is done with a Chemex so I normally just give it a good swirl after it's finished brewing to bring the temp down. That's hands down the worst part of brewing with a siphon, it takes so damn long to cool to drinking temperature.
The heat loss would definitely be my main issue with those. Though I go a bit far the other way in that I boil water, pour it into my gooseneck kettle, then pop that on the hob to get the water back to boiling to ensure there's no thermal loss to the kettle itself. Then again, I guess the plastic doesn't soak that much heat.