Are there thermo bottles to store tea, as soon as it is made (100ºC/212ºF)?

You don't need anything special for that. I have often made tea in a regular thermo bottle, with no adverse effects on the bottle. It does help that it keeps the tea hot. So the fancy one you linked is probably OK too.

If you want a lighter bottle, you can see if a glass bottle doesn't weigh less, although a thermo bottle from thin stainless steel isn't that heavy compared to glass. Glass should withstand boiling water without breaking, if the bottle isn't too thick and hasn't been held in a very cold place (room temperature is OK). It still can shatter, so you should probably take precautions (pour over the sink), although the chance is very low.

A typical softdrink bottle shouldn't be reused for tea, even if it doesn't melt outright it is likely to get very soft, etc. But some plastic bottles will be OK with hot liquids, for example Nalgenes should do the job. They have the advantage of being wide-mouthed (it is very hard to clean a glass lemonade bottle because of its narrow mouth).

You can go to the local hiking store and see what they have, and whether you like it more or less than a thermo bottle (and they will have thermo bottles too). Their bottles are optimized for easy caring, and some come optionally with a neopren sleeve to keep the temperature longer.

There are tea tumblers/Thermos bottles which come with built-in infuser baskets, so you can steep loose-leaf tea straight into them, and then sip from the top. They're explicitly designed for this use.

If you are near an Ikea store they have perfect 32oz thermos' for $15. I buy like 1 a month and have about 10 now. I make all my tea on a friday night and then it is cool by Sunday. I steep it and then put it right in the freezer ( I like cold tea). But I found that with Green tea if you let it sit the tanins come out and it gets brown and loses its taste.

In my experience, if tea is stored for any length of time, it goes "off"... It takes on an unpleasant stale flavour, and the colour changes from bright reddish-brown to a more greyish colour - which is particularly noticeable if you add milk.

I never put tea in a thermos - I find it better to take hot water (really hot... straight from the kettle into a pre-heated insulated flask) and some teabags, and make the tea when needed. It isn't perfect, since the water is usually a bit cooler than it should be (not boiling) but the result is much nicer than tea that was made several hours earlier.

Why this happens I am not sure. I imagine it is some kind of oxidation reaction, but I could be wrong.

It is even worse if you try to store tea with milk. It goes nasty in a quite a short time - half an hour or so. There seems to be some kind of reaction between the tannins and the milk.

I understand that iced tea is routinely stored for hours, so perhaps it is not affected in the same way. Maybe the temperature is part of the problem.