Why is the temperature of the water important to get rid of mixtures?
Water temperature can be judiciously used to get rid of mixtures. We can make use of "solubility" of substances in water and how it varies with temperature. Among the mixture there would be some components that will be water soluble and the rest would be insoluble.
(Since further information is not given in the question, I am assuming that mixture is solid, i.e. made up of various materials in solid phase). So when the mixture is dissolved in water, some components will dissolve and the rest will stay insoluble. Solubility is a function of temperature and the higher the water temperature, the greater will be the solubility of a substance in water. You can try this with adding salt or sugar to water: you will notice that you can progressively add more salt or sugar to the water as its temperature goes up. So by heating the water, we can ensure that all the soluble materials are dissolved completely. And afterwards we can filter out the insoluble fraction of the mixture. The soluble components of the mixture can be separated based on the temperature at which they dissolve (although it would be slightly tricky and one has to be careful about temperature).