High pitch whine upon startup

[FiST Augustine]

So I admit I am relatively new at owning this car, I have only owned it for about 5 days now. Tonight it started to make an odd sound I hadn't heard before. After work, I started it up and I admit I accelerated a little fast before fully warming up, but maybe like 0-20 at 2/3 throttle. I should have let it warm up more. But I noticed a high pitch whine. I turned off the a/c and still heard it. It didn't matter if I accelerated or idled. It continued until I stopped for gas about a mile down the street. I was thinking it sounded like a fan maybe but the past week it has been 100 degrees without this noise and tonight it was only 84 degrees and it had been sitting for 8 hours. Is this a normal sound? I tried searching online but wasn't sure if I found anything that exactly matched this. It sounded like when I owned my Prius and the cooling fan would sometimes spin up really fast by the back seat and make a loud whine whenever it was really hot to vent the batteries but only louder.