Why is it impossible to heat the room with candles?
Wiki says, that the hottest part of a candle flame burns at around 1400°C, while the average temperature is usually 1000°C. And I will be happy to get only 20°C of that heat in my room. So I think it should be possible, because warm air rises, and cold air comes from below constantly. But in fact the candle does not heat well, even if i use many candles to increase the heat it won't help much.
So, where does all this heat disappears?
Temperature is not the same as heat. A candle flame has a very high temperature, but the substance which is actually hot is a thin gas. As a result, the total amount of heat being produced by the candle is quite small - a quick google search suggests that a typical candle might generate somewhere on the order of $50$ to $100$ joules of heat per second.
Even a small space heater would typically generate 10 to 20 times that amount. So the answer to your question is that it isn't impossible, you'd just need quite a few candles.
As another answer says, heat is different from temperature. Think about the bright blue arcs you get between your finger and the doorknob when you get carpet-shocked in the winter. Those sparks are blue because they are hotter than the surface of the sun. But the total energy involved in a carpet shock is a few millijoules. It’s the energy you care about, not the temperature.
Another answer also claims that the thermal power of a candle flame is 50–100 watts. That’s comparable to an old incandescent light bulb. Like a candle flame, those bulbs were too hot to hold while they operated. But you had to really pay attention to decide if a single light bulb was really heating up a room.
A kilowatt (ten hundred-watt candles) is the usual power of a small electric stove burner. (The big burners are usually 2500 watts.) You don’t ordinarily think of boiling a teakettle as an activity which warms up your house. But imagine boiling a teakettle, then pouring the hot water into a hot water bottle, and boiling another kettle, to fill another hot water bottle, all day. Eventually, your first hot water bottle would be cool enough that you could put that cooled water back in the teakettle instead of getting fresh water from the tap. That’s an idea of how much heat you could really extract from some candles.
A suggestion I have encountered for winter blackouts (which you mention in a comment) is to get some empty terra-cotta flowerpots from your garden shed, and put them upside down over a candle. Leave a gap underneath for fresh air to come in, and the hot exhaust can escape via the drain hole in the planter. I have tried this. There is a sweet spot between the little flowerpots which get too hot to hold, versus the big ones that you can’t really tell whether they have gotten warmer or not. I certainly didn’t feel like having a hot flowerpot upside down over a candle on my dining table made my room noticeably warmer. Water is probably a better material for storing heat than terra cotta anyway.
