Blue is not “cold” and yellow is not “hot” — it is the other way round
Ask anyone in a kitchen and they will tell you a yellow flame is a strong flame. It is the most expensive sentence in the room. Methane and propane burn colourless — a fully burnt flame is almost invisible in daylight. What you see as blue is not soot at all: it is the chemiluminescence of intermediate species, CH and C₂ and excited CO, in the inner cone. What you see as yellow is solid carbon particles, heated past about 1000 °C, glowing by blackbody radiation. Those particles exist for one reason: there was not enough oxygen to finish the job. A yellow flame is a flame with unburnt fuel in it, and the same shortage that makes the carbon also makes carbon monoxide. Soot and CO are two outputs of one cause, which is why the bottom of the pan is the best evidence in the kitchen.
So the gas arrives, but gas on its own does not burn well. It has to be mixed with air first, and that happens inside the burner: the gas leaves the jet at speed, the jet crosses a throat and drags air in with it — the venturi effect — and the mixture travels up to the ports already part-mixed. That dragged-in air is called primary air, and the adjustable shutter over the intake is the damper. Too little primary air and the flame cannot finish burning: yellow, sooty, CO. Too much and something else happens — the mixture leaves the ports faster than the flame can travel back down into them, so the flame lifts off and floats, or blows out entirely.
That gives the single most useful idea on this page: the damper has a window, and it fails at both ends. Everyone who discovers the damper does the same thing — turns it until the yellow goes away, then turns it a bit more because more air must be better. Then the flame detaches, and sometimes it goes out and relights with a pop, which is a small explosion in the kitchen. Set it by watching the flame, not by turning until it stops.
Three faults, three answers
The whole flame is yellow and the pan is black underneath is not enough primary air. Three causes, in order of likelihood: the damper is closed too far, which is common after a move, a deep clean, or a change of gas; the jet or the venturi is clogged with carbon and grease, which both narrows the jet and spoils the entrainment; or the cap is deformed so the mixture escapes somewhere it was not designed to. The hard evidence is the pan, not the colour — everyone's idea of “yellow” is different, but soot is soot. Open the damper in small steps and watch the flame shorten and turn blue at the root.
Only one side of the ring is yellow is local, not a chain problem. Ports blocked by spilled sauce or grease reduce the flow on that side and spoil the secondary air around it. A cap that is not seated, or is warped and lifting on one side, lets mixture escape through the gap instead of the ports. The free test that separates the part from the position: turn the cap through 180° and put it back. If the yellow sector moves with the cap, it is the cap — blocked ports or warping. If the yellow stays where it was, the cap is innocent and you are looking at the jet or the venturi on that side.
The flame floats above the ports is too much primary air, or too much pressure. Either the damper has been opened past its window, or the regulator is delivering more than the jet was sized for — a fresh cylinder, a cold snap changing the propane fraction, a regulator on its way out. It is the more dangerous of the two failures, because a lifted flame can go out locally while gas keeps flowing, and then relight. Look at the root of the flame: a normal flame is attached to the port; a lifted one has a visible gap and a pale blue-white root hanging in the air.