No, angelfish cannot live without a heater. Angelfish are originally from the tropics and need warm temperatures of around 75⁰F – 81⁰F (24⁰C – 27⁰C) to thrive. Suboptimal temperature can result in growth stunts, illnesses, and even death.
Even if the tank is located in a warm room, the temperature can still fluctuate. That’s why you need to install a heater in your angelfish tank.
You should consider getting an adjustable heater so you can maintain the water temperature properly. Also, submersible heaters are preferable because they’re more stable and can heat the tank evenly.
Lastly, make sure to keep your tank size in mind. A larger tank requires a heater with higher wattage.