Much of the flavor and aroma of tea comes from volatile oils/compounds.
The heat applied to tea leaves while steeping them is key to releasing those volatile compounds but when you reboil the tea, a large portion the flavor compounds in the water are likely just going to be vaporized. The end result is the reheated tea will have very little 'tea' flavor left. The tannins however are less volatile and remain in the re-heated tea hence the bitterness.
A pre-warmed ceramic teapot would probably due the trick for keeping your tea warm for 5-10 minutes.
As you've noted in your description of your experiments, there are many variables (e.g., amount of tea, type of tea, steeping times for each infusion, etc.). Fundamentally, the type (green/oolong/pu-erh/etc., quality, nature) of tea is a huge factor, and personal preference is a factor but not the only factor (what you describe as "bland" or weak might not be to someone else). I think there are some objective generalizations, though.
The tea you start with matters. A specialty tea dealer will often annotate a given offering with brewing recommendations (e.g., commonly temperature, time, quantity of leaves per cup, as you note); some dealers will also suggest that the tea can be enjoyed through 2-3 or multiple infusions. Such a tea is a great place to start for your own experiments. I find that some teas (e.g., darjeeling, broken orange pekoe) simply infuse too quickly and to fully in the first infusion that they are totally spent. Further infusions are weak and bitter.
Some teas that I find work well for multiple infusions:
- good quality green-oolongs (multiple infusions; tung ting or formosa)
- green-white blends like white peony (2 infusions)
- lightly roasted/toasted green teas, like long jing (dragon well) or gunpowder green (aside: this is probably a good place to start as it can be inexpensive and enjoyable)
- higher quality pu-erh teas.
Techniques. This varies per the type of tea; but in general, I personally do the following when I intend to infuse loose tea multiple times:
- Infuse slightly more tea (perhaps 50% (1.5 times) more; certainly not 2-3 times);
- Infuse for a shorter period of time (perhaps 1/2 to 2/3 as long) on the first infusion;
- Infuse for progressively longer amounts of time for subsequent infusions.
- If anything, slightly lower temperature on subsequent infusions.
That tends to make the resulting brew (to my taste) slightly more uniform in result, though there is significant difference in flavour.
Other things to keep in mind: if you're using tea with caffeine, most will come out in the first infusion; if you're using 2-3x the tea, this is significant! As you also note, the character of the brew can be very different through the several infusions. This can be part of the enjoyment, as each infusion will extract different ratios of "stuff" into the resulting brew. For lower-quality gunpowder green teas, for instance, I actually prefer the second brew over the first.
Instead of multiple infusions, you might also simply
- consider brewing a larger pot all at once into a thermal carafe, then enjoying it a cup at a time.
- consider brewing just a cup at a time, which will have a better result for certain teas (a pathological example: bags)
I would not recommend some things that you said: most specifically, I don't think you'll get benefit from infusing at a higher temperature for subsequent brews; this is likely to give you bitter or off-tastes; you're "burning" the tea and extracting stuff you don't want.
Best Answer
There are couple of factors at work when re-steeping green tea: temperature, time, and the quality of the tea (the size & way it's been processed). Green tea is supposed to be brewed with water that's been brought to boil and allowed to cool to 167 - 176 degrees Fahrenheit (though many people simply heat the water to that point or what they eyeball as hot but not boiling). Green tea is typically steeped for 1 - 2 minutes. And green tea, especially loose leaf, but also with higher quality tea bags, has furled and sometimes rolled leaves. The lower temperature, the short steeping time, and the curled leaves mean that flavor is still left within the leaves even after multiple steepings. The leaves continue to expand and release in subsequent baths. I don't, unfortunately, know any of the exact science--what's being released when, etc.
However, a possible alternative to boiling & brewing individual teas when done or simply using more tea (the typical choice when brewing larger quantities), you can bring your water to temperature, steep, pour it into a preheated or heat retaining container, and repeat the cycle until you've brewed your multiple cups in one go. As far as I know the tea leaves don't need to 'rest' in between brewings.
The reason green tea can be re-steeped is also the reason most black teas can't. Black tea is subject to boiling water for a longer period of time (typically Western use is 3 - 5 minutes; some cultures favor an even longer steep for the deeply bitter tannins). The hotter and longer steep pulls more flavor out of the leaves faster. Some black teas, especially high quality whole-leaf, can be re-steeped, however. Most bagged black teas--and a lot of loose leaf--can't.
The heat & steep time is dictated by the processing of the tea once it's picked. Green tea has minimal processing--pluck, wilt, shape & dry. Black tea is allowed complete oxidation (called fermentation). Fermentation breaks down chlorophyll, releases tannins, and forms many of the taste & aroma compounds that typify black tea. Oolongs and other varieties are subjected to varying degrees of fermentation. The size & shaping of the tea leaf--allowed to remain whole, broken, rolled, or (for most bagged tea) cut into fannings and dust, also affects how tea should be initially steeped and whether it can be re-steeped. Highly rolled oolongs, for example, often hold up to more steepings than green tea and are even said to taste best only on the 3rd or further steeping.