Is it recommended to rinse the teapot with boiling water, or does that make no difference?
Preheating the tea pot with hot water will also prevent the tea pot from cracking when you do add boiling hot water for the tea to steep in.
I will say that I have a fairly thick-walled tea pot, I rarely preheat it, and I've never seen any danger of cracking. However, if I had a nice china pot, I would preheat it. Better safe than sorry!
The main reason you put boiling water in the teapot before making tea is to heat up the teapot. You dump out the now cooler water and then add your teabags and more boiling water, and the teapot will now be warm and not leech out the temperature from within it. This results in tastier tea, but is totally not necessary if you didn't make enough hot water, or don't want to spend the time doing so.
My mother and father were raised and lived in Wales and England from 1903-1923. The homes were quite cold in the fall, winter and spring. If you put boiling water into an extremely cold teapot it would crack and weaken the pot. I have been trained to do this even when it is in the warmth of summer. I have noticed that if someone pours boiling water into my bone china tea cups or mugs, that they will crack. The china cups and tea pots should at least be at room temperature otherwise a warm rise is required.
Assuming it's clean beforehand, the only reason I can think to do this would be to keep the water hotter longer by heating the pot a bit (or, if it's a ceramic pot, to prevent the glaze from cracking...I certainly wouldn't use boiling water for that though).
Tea should steep well before the water is too cool. I don't see any reason to rinse the pot.
I don't remember whether I've ever seen a teapot or cup break apart the first time it was filled with boiling water. But I have seen cups develop cracks. Being wide open at the top, it's easy to see a new crack in a cup. Pots are a different story. The small openings limit both light and sight, so cracking may not become apparent until it works its way to the outside. Once it works its way through, it will just keep getting bigger and the pot weaker.
I imagine none of us remember seeing a pot break apart because of modern improvements in the chemistry, molding, firing, and handling of china. With fewer faults in the finished clay, the effects of rapid heating aren't so severe. But an old-fashioned pot or cup deserves gradual pre-heating for two reasons. The liklihood of faults due to manufacturing of older goods is one. The liklihood of hidden damage due to long use is the other. When you bring a teapot home from an estate sale or an antique shop, you may not be able to tell if there are already cracks inside the pot. There may even be hairline cracks on the outside, so fine that you can't see them easily. Whether inside or out, the cracks will surely suffer from boiling water unless gradually preheated.
I've come up with a quick and energy-efficient way to gradually preheat a china pot or cup. While the kettle is on the fire, I put a small amount of cool tap water into the pot or cup, then pop it into the microwave for 20 to 60 seconds, depending on size. When the kettle is ready, the pot or cup is ready.
Nuking a pot or a cup might seem like drastic pre-heating, but it is slow-w-w-w by comparison with the instantaneous heating that comes with boiling water.
This is tea-tasters' lore, on the basis that the best flavour is extracted from the leaves at a temperature as close to boiling as possible. Heavy ceramic pots will absorb a lot of the heat from the water unless pre-heated, and a cooler extraction will be less efficient. This is less important with thinner metal pots where heat absorbtion is less.