A block of ice as big as a room will have more thermal energy than a cup of hot tea.
But the tea feels hotter because the average kinetic energy (temperature) is higher in case of tea.
I conclude from this that total energy doesn't matter when it comes to what feels hotter.
But it is said that steam at 100 °C feels hotter than water at 100 °C because steam has more energy, which is contradictory to my conclusion.
Please explain where have I gone wrong.
To resolve the confusions: When we heat water, its temperature keep on increasing. Boiling starts when it reaches 100 degree Celsius and bulk vaporization takes place. These vaporised molecules, possessing same energy of water (is at same temperature as it) plus latent heat of vaporisation, is what I am referring to as steam. So, it has more energy but same temperature.
I expected no confusion regarding such steam causing more severe effects. But now that it has, let me mention that this is a common secondary textbook fact, that is taught and studied in India. Here is a link to a related school material: https://byjus.com/questions/what-produces-more-severe-burns-boiling-water-or-steam/.
Best Answer
TL;DR: You have probably not been exposed to 100°C water in either phase and even if you had, you could not have reasonably felt its temperature on account of receiving a third-degree burn. Hot water and steam are both dangerous but fundamentally different, so comparing them is like gorilla vs. shark.
I am not exactly sure what you are comparing here, but if you take a sufficiently large piece of your skin and expose it to 100 °C water (in either phase) for a sufficiently long time for your temperature sensors to actually give a reasonable result, you would suffer from a severe burn. In this case, I have several reasons to distrust your reports about what temperature you feel. (Note that by feel, I refer to your direct sense of temperature and not to the effects of the resulting injuries and similar.) For example, this Healthline article reports 1 s of exposure to 69 °C water to be sufficient for a third-degree burn, which destroys your nerve endings and thus is mostly painless on the long run (and I doubt anybody can distinguish the nuances of extreme pain occurring before).
Now, what did you actually experience?
Sipping a cup of hot tea doesn’t give you 100 °C water. Even if you brewed the tea with boiled water, the latter probably wasn’t homogeneously 100 °C to begin with. It then cooled down during brewing the tea, pouring and through contact with the cup. Sipping brings a very small amount of water in contact with your skin that gets cooled down through contact with skin and air rapidly (on account of being so small). On top, you may have an additional protective layer of saliva or similar that needs to heat up before anything important does (pointed out by Shmuel Newmark). What your temperature sensors perceive mostly depends of the amount of water.
I am not sure what your steam experience is, but immersing any part of the body in pure 100 °C gaseous water is pretty difficult (and dangerous). The steam that forms above pots or kettles with boiling water and anything else that is colloquially called steam is a mixture of gaseous water, air, and liquid water droplets. The latter is what you can actually see; pure gaseous water is transparent. Conversely, if you can see it, it’s not pure gaseous water, and I would be impressed if you actually managed to temperature-sense that with your skin. Instead, if you boil a kettle of water, the steam that comes out has already considerably cooled down due to contact with the air and other factors. It can still cause severe burns though. If your exposure is sufficiently mild that it doesn’t, it depends on the details, i.e., how hot was the steam and how much was it, etc.
In general, your temperature perception depends on the amount of heat deposited on a timescale relevant to your heat sensors. This in turn depends on:
Water vapour in air does not have to be at 100 °C or hotter. Rather it has the temperature of the surrounding air. You can think of it as water dissolved in air. It exists at all temperatures and causes (or rather is) humidity. The amount of water you can dissolve in air depends on the temperature.
Now due to changes in temperature, it can happen that a portion of air has more water dissolved in it than it can hold. In that case, the water condenses to droplets you see as steam, clouds, or fog – not there is a fundamental difference between those. If you boil water, you do indeed release packets of 100°C water vapour into the air, but these immediately cool down when mixing with the air, which causes condensation leading to the visible clouds we usually associate with steam. Those are not 100°C hot (and nothing inside them is); if they were, your air would also have that temperature and you would not see much. (The heating also causes an upward flux of air, which carries those droplets with it and avoids them returning to the water immediately.)
Both, boiling water and hot steam are pretty dangerous and how dangerous exactly depends on how long you are exposed to how much of it at what temperature and more. As one is a liquid and one is (mostly) a gas, encounters with them are not directly comparable (as opposed for example to putting your arm in two different liquids). You might as well ponder whether a gorilla would win a fight against a shark. We might look at how much reported injuries we get for either, but that says more about how careless people are around the respective substances.