No, ghost shrimp cannot live without a heater. Ghost shrimp need a warm temperature of 65°–80°F (18.3°–26.6°C) to thrive.
If the water is too cold, their metabolism might stop and cause them to die. Similarly, if the temperature is too hot, they’ll molt way too often, leaving them vulnerable to diseases, bacteria, and parasites.
To prevent the water temperature from fluctuating too much, you should install a heater and a thermometer. Make sure to pick the right heater according to the tank size. The larger the tank, the higher the heater’s wattage should be. For example, a 20-gallon tank will need a 100-watt heater, but for a small 10-gallon tank, a 50-watt heater should suffice.