It's more about when it idles the fan for the heater seems to act like it's running out of power.
If you're seeing symptoms of power loss or jumping while running, get your alternator checked out. Radio and dash dimness changing with accelerator inputs, headlights getting dimmer and brighter, HVAC fans getting stronger and weaker based on accel...stuff like that. Alternator will kill batteries as well and will leave you stranded on the road when it completely fails.
That said, six years is end of life for a normal car battery, too. It had a good life if it's still running now.