X5 4.4 Starter 'whirs' then starts - no clicking

[253movingto928]

Is my starter going bad?

2005 X5 4.4 166,000 miles.

I live in Havasu, Arizona and it never really gets cold here - maybe 70F in the morning and during the summer it can hit 115F on a regular basis.

In the morning, I turn the key to start it and the starter will make a 'whirring' sound for 2-3 seconds then turn the motor over and it starts. There have been a few times, I turn the key off then back to start and it starts fine. Seems when the car is warm/hot and I run into the store for 5 minutes and go to restart the car, the whirring problem goes away and it starts right up.

Also about 2 weeks ago, I noticed while idling at a stoplight it idles kind of rough. - I did throw a bottle of injector cleaner in the tank to see if that helps but the rough idle at idle is still there.

Battery is a bit over 2 years old - longtimers in this town, say batteries should be replaced every 2 or 3 years due to the heat. - car is always outside.

Voltage before starting: 12.19volts - voltage at idle: 14.4volts - I replaced the alternator 2 years ago.

There are no 'clicking' sounds from the starter when it does not start, just a whirring noise.

Any connections to the rough idle at stoplights? Any other ideas?

Thanks