This is two different things: thermal mass and conductivity.
The moisture you give your fingers to put out the candle provides them with enough thermal mass to absorb the energy from the candle, without dramatically changing the temperature of the water (the water can absorb a lot of energy without changing temperature) Also the water is a better conductor than your skin, so it spreads the energy across the liquid much better.
When you wet an oven mitt, you turn what should be insulating you from the heat into a better conductor, and the heat travels through the water in the glove to burn your hand.
Warmth and temperature are not the same thing.
A candle might be a few hundred degrees, but it doesn’t radiate (much) thermal energy. The wet on your hand will be enough to quell that intense – but small- energy source.
But the hot pan, despite having a lower temperature, is larger, and had more thermal energy in its metal/Pyrex structure. That abundance of heat is enough to shluck through a wet mitt through conduction. The heat from the over pan cannot be quelled by a soggy mitt, so instead that thermal energy agitates the water, making it hot, and soon enough the heat conducts through.
A good mental thought experiment that could help with understanding is to ask “How much volume of water will it take to cool down this hot object?” Framing a question like that makes you begin to consider the energy content of the hot object, not necessarily its temperature.
In fact, it is known that the temperature at the hottest part of a candle’s flame can be up to 2,500 °F, yet the flame could be put out by a single drop of water. Hence a wet finger is protected when touching a candle flame. But you can imagine that a hot pan out of the oven will be barely affected by a drop of water. The hot pan has tremendously more energy content than a flaming candle.
If you take an iron pan out of the oven and throw water on it, it will immediately will turn to steam. FWOSSH! The same thing happens when you put a damp mitt on it. The water in contact with the metal will turn to steam very quickly and hit your fingers super hot. It depends on the ratio of the metal type, how hot it is and how much water the mitt is holding. If you have a lot of water and low heat, you are fine as the water can take it without turning too hot or even flash into steam. But if you have lots of heat and low water, the water will be “overwhelmed” and burn you.
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