Its possible that when you drink a hot liquid, you swish it around your mouth a lot less than when you drink a cold liquid, and thus fewer of the taste buds on your tongue are exposed to it. This wouldn't be surprising: it's hot after all.
Another possibility is that if you're starting with hot coffee, and adding sugar to it, that the sugar isn't fully dissolved when you drink it hot (it takes time, especially if you don't stir it much), but has dissolved by the time the coffee cools. With more dissolved sugar, it is sweeter.
I've been drinking loose-leaf tea at work for many years now, and have gone through most of these.
- cup with a ceramic or glass strainer.
I've tried both the ceramic type with holes and the glass type with slots. The mesh is never fine enough for me. In addition the holes or slots invariably get packed with leaves and are a pain to clean.
If you mean the tea-ball type, I can't comment. But a steel mesh strainer is my absolute favorite. I've been using the same one (pictured below) for years now and have never noticed any off flavors. Easy to clean: just dump out the leaves and give a good rinse, picking or sponging out the occasional stuck leaf.
Not microwaveable, but you don't want to microwave the leaves, anyway. Microwave the cup with water in it (put a stirrer in to avoid superheating the water. Yes, it can happen, and has happened to me), then put the strainer in when it's the right temperature.
I have never used one, so I can't comment authoritatively, but it seems like at the least they'd be harder to clean.
- fillable disposable tea bags.
I hate disposable anything. I tried the type of bag pictured below and they were a pain. They tend to wick tea out of the cup and onto your table.
As for the other gizmos, I think for tea, simpler is better. The above are the only methods I've used, and I find the mesh basket is far and away the most convenient and best solution.
Best Answer
Tea and Coffee contain a spectrum of flavour compounds and most certainly, not all are pleasant.
If you've ever had an over steeped tea or over brewed coffee you'll know that the optimum extraction point is long before maximum extraction. Where you are no longer extracting just pleasant compounds and picking up higher concentrations of things like caffeine, bitters, etc.
Agitating tea or coffee runs the risk of (or facilitate) reducing the time it takes to extract the unpleasant part. On that front, experiment with not yo-yo dunking tea bags and squeezing the tea-bag with the back of the spoon (mild forms of agitation) to see the taste difference.