I want something I can quickly throw over a thin cotton shirt
I don't think I can do electrics
Its not that cold here in california
You want something you can throw over a T-shirt for cold riding? The only thing I can think of is a one-piece snowmobile suit, and that won't have armor or abrasion resistance.
Your legs may not feel cold, but you're losing heat through them nonetheless. You'll probably want windproof pants. Even Cordura ski pants would help a lot. One with side zips or snaps will go over your riding boots as easily as they go over ski boots.
The FG Kilimanjaro would be a good cold weather jacket, but the FG Voyager II is better. It's an obsolete model, but it's got wind cuffs at the waist and wrists, a wrap-around neck/chin gaiter (very nice) and is completely windproof. If you can find one on eBay or elsewhere, they're going for around $100-$150.
Windproof fleece is an excellent insulator for cold riding. Cabela's sells a brand called "Windshear" that works very well. One layer of that is probably worth two cotton sweaters.
Electrics aren't just for very cold weather riding; they make everything that's less than 70 F much more pleasant. An electric vest or liner is much less bulky than a sweater and actually puts heat into you rather than trying to slow it coming out. Failing that, heated handgrips are also very nice, and also not just for the very cold. And you don't have to put those on every morning.
Sealing out the wind will be your first priority. A balaclava works better than a bandana or scarf around your head and neck. Make sure your glove gauntlets close around your sleeves. Watch the small of your back; short riding jackets can let a breeze up there.
If I were you and had a bit of money saved up for cold weather gear, I'd get the following:
-a good balaclava that fits under my helmet
-a completely windproof jacket, be it a moto-specific one, or just a windbreaker for my leathers
-snowmobile gloves or similar
-windproof pants
-an electric vest or liner
Bang-for-the-buck you can't beat a windbreaker and balaclava for lowering your temperature limits. But electrics are wonderful.
Dave