Recently when I start the car (usually when outside temperature is less than 70F), I hear a slight to moderate grinding sound right as the car starts.
Nothing else seems out of place during the starting process and the car behaves as expected otherwise. I'm guessing there's something going on with the starter, but I have no other ideas.
The battery is fairly new. It's a 6-speed manual transmission 4-cylinder.
Going by the sound that you have posted I would think it is the starter gear being slow to retract from the flywheel and the teeth getting hit by the teeth on the flywheel as the engine speeds up and the starter rotation slows down. Solution : remove the starter and make sure all the solenoid / lever / gear mechanism moves freely.
Thanks for the audio.
By hearing the sound it doesn't seems that there is a problem with the engine. Neither there seems to be problem with the starter mechanism.
At temperature below 25-C/77-F the capacity of the battery decreases i.e. the terminal voltage output drops.
So as you said that this happens when starting at lower temperatures, it is quite possible that the starter motor is not getting enough voltage to crank up the engine due to which it making that sound (same phenomenon when battery dies.).
Try starting you car in a warmer environment and see if the problem still persist. If not not then there is nothing to worry and if the problem still persist then you should consult mechanic based on @Solar Mikes answer.
