Extended heating can cause pyrolysis of sugars and evaporation from wells changing the volume. Still the main reason is the absorbance of the generated product changes with temperature (https://pubs.acs.org/doi/pdf/10.1021/ac60147a030?src=getftr).

The ice is just to reduce cooling time.

Hello Cha Joonseo

On heating the alkaline mixture of reducing sugar with DNS at elevated temperature (100°C) for 10 minutes, the reddish-orange color will develop, and at this point it will show a direct relationship with the concentration of the reducing sugar in the sample. The color developed is maximum at this time point (10 mins) which is standardized for this assay.

So, to stop the reaction immediately, the tube is dived in cold water. When the tube reaches room temperature, 300ul of the resulting reaction mixture is transferred to the well of a microtiter plate and the absorbance read at 540nm using microtiter plate reader.

So, when you use ice, it will cool down the sample quickly so as to stop the reaction in the tube.

Best.