While walking around in my engine compartment, I noticed the t-stat is not connected. The flapper is spring loaded and in the HOT position ( right? ).

Will I have any problems other than slower warm-ups?

People will certainly have different opinions on this.
As I understand it, you will have shorter engine life and worse gas mileage since your engine may spend a lot of time running too cold.
It is quite common to leave them disconnected, but it's also quite common for engines to run poorly and suffer early deaths.
Just my 2°

No you don't need one, yes you should have one.

i have mine disconnected and glued down so it always stays full open.

dunno. i don't drive just to the corner liquor store and back so the car usually get's warmed up OK.
plus, it doesn't get all that cold here in CA anyways.

to me, it seems like just one less thing to worry about.

it's not like our engines like to run too hot or something,
Andy

that, i'm not sure about!!!!

mine are glued DOWN (which is the hot position) to make sure they stay there.
Andy

Hi,
I'm pretty sure they fail to the "hot engine" position. This is incase the wire breaks. If the wire breaks, you may not know about it until the engine gets really, really hot!
Cheers, Elliot

I guess I meant to say if the wire breaks in the "engine cold" position. Thats why it fails to the hot position. Anyway, I agree. You don't need it but ya should have it.
Elliot

Elliot, I hope you mean that a broken t-stat cable leaves the car in a safe position with max cooling available full time.

for some reason, i thought it was the OPPOSITE ...

you better check
flaps need to be DOWN for max cooling ...
Andy

The car NEVER overheats...Even when I give it the beating of a lifetime!

I can move the flaps by hand and they always snap back into "The Position".

They fail in the open position. The thermostat on my car was disconnected when I bought it. It doesn't get that cold here either but the car runs way better with the thermostat installed.

Okay. It fails in the "max cool" or "engine hot" position. When the engine is cold it restricts cooling air. When the engine is hot it allows max cooling air. I thought about rigging mine up with a manual adjustment like an aircraft cowl flap. With my luck though, I'd forget to open it and roast my new motor. I installed a new cyl. head temp. gauge that works pretty neat. Easy intallation. Highly recomended.
Cheers, Elliot