Problems with increasing heavy metal contents in natural waters are becoming a global issue. At the same time, improved methods for water treatment are becoming increasingly important. In this context, natural zeolites can be used to purify polluted water. In this paper, we investigated how the adsorption capacity of natural zeolites can be improved. Natural zeolites from the Shankanay district, Almaty, Kazakhstan, were used as adsorbent material for experiments on improving the water treatment of heavy metals. We found that the adsorption capacity for heavy metals was increased greatly by thermal activation using furnace treatment. The optimal thermal activation condition was about 550 °C for a duration of 2 h. However, the improved adsorption capacity for different heavy metals varied depending on the heat treatment temperature. Adsorption by the heat-treated zeolites at a temperature of 550 °C was 87% for nickel, 99% for copper and cadmium, and 100% for lead. Adsorption by heat-treated zeolites at a temperature of 500 °C was 78% for nickel, 98% for copper, 83% for cadmium, and 88% for lead. The residual concentration of heavy metals in the filtered water did not exceed the maximum permissible concentrations for drinking purposes. In all experiments, intense adsorption took place during the first 10 min representing 35 to 61% of the metal ions in the water. Adsorption properties were verified using adsorption capacity (BET), IR spectroscopy, and scanning electron microscopy. The study shows that modified Shankanay natural zeolites have great potential as a low-cost adsorbent material for purifying water from heavy metals.