Yes, mollies need a heater. Mollies are tropical fish, so they need a warm temperature of 72°F to 78°F (22.2°C to 25.5°C) to survive. Despite being hardy, mollies can’t tolerate sub-optimal temperature very well. Sub-optimal temperatures can result in growth stunts, illnesses, and even death.
Even if your tank is located in a warm room, the temperature can still fluctuate throughout the day. You should get an adjustable heater so you can maintain the water temperature properly. Don’t forget to install a thermometer so you can easily monitor the water temperature.