Imagine a plastic sac filled with water placed in a pan of boiling water. I wonder why the water inside the sac does not boil. The temperature of the water inside the sac should be the same as that of outside water, i.e., 100 deg. celsius.
Similarly if to place a glass tumbler of water inside a pan placed on fire, the water will boil only inside the pan, but not in the tumbler.
Best Answer
Both bodies of water will heat till 100 C (as well as the vessel). Then, the outside one will start boiling by taking latent heat from the surroundings, Now, we only have heat transfer due to conduction/radiation when there is a temperature difference (or an emf, but that's irrelevant). It's mainly conduction we need to consider, anyways. Convection won't get heat across a solid. Now, there is no temperature difference across the vessel, thus no net heat transfer. If we placed cooler water inside, there would be enough heat transfer to bring it to 100 C, and then it would stop (we can't boil pure water below 100 C at 1 atm)
So the sequence of events is as follows:
Of course, since it's steam, it will probably diffuse out, so eventually only a tiny bit of the inside water will boil.
In fact, this is one of the ways one can keep a fixed mass of water at exactly 100 degrees celsius. Useful for making extremely accurate calorimetric calculations.