The answer to your questionnot really lies in the chemistry of solubility but in the biology! Generally, cold suppresses sweetness. As an example, consider soft drinks that are usually served cold: they taste sweeter when warm (like you said with your example of kheer).
Our taste receptors send a stronger signal to the brain when activated by warmer substances and so the perception of sweetness, in this case, is lessened when we consume cold food or drinks.
Thereare taste receptors on the surface of our tongue which refer to the proteins TAS1R2 and TAS1R3 which, which bind to the “sweet-tasting” molecules. When the molecules bind to the receptors, they trigger a series of actions which increase the number of positively charged potassium ions (K+) in the cell to which the receptor is attached. In order for the signal to continue along to the brain, the cumulative positive charge of the potassium ions must be high enough to activate a TRPM5 channel into the cell, so that calcium ions (Ca2+) can pass through. The Ca2+ions are required for the release of neurotransmitters which send the signal. This channel requires a much lower positive charge for activation when it is warm than when it is cold.
Now if you were to put, e.g., a cold coke into your mouth, it decreases the temperature of the entire tongue and consequently the TAS1R2 and TAS1R3 proteins, and the TRPM5 channel. This will result in it requiring a greater positive charge in order for the signals to travel to the brain. This means overall also less signals are even received by the brain, thus resulting in us perceiving less sweetness. Hope this cleared your doubt :)