Should red eared sliders have a heater in their aquarium?

Not a heater, a heat lamp. In the wild, turtles bury themselves deep in the mud and hibernate during the winter months. Obviously, this isn't possible for a turtle who lives in a tank. It is dangerous and unhealthy to let a captive turtle go into hibernation.

A UV heat lamp will simulate the summer sun and provide the Ultra-Violet (UV) light that your turtle needs, so the turtle will stay warm and go through the winter without hibernating. You can buy a UV heat lamp to put/hang over the tank at most pet stores, including Petco. You can even buy a timer for the tank (not at Petco, though, for some reason), so you don't have to be home to turn it on every morning, and off every night.

I have included two links: one to the Petco page where you can buy Zoo Med Reptile Basking Spot Lamp bulbs, and a lamp to put those bulbs in. The other is to a website called X10.com, where you can buy a timer for the lamp.