Just bought a used Prius!

Welcome aboard and enjoy your ride! Not sure about the key issue.

 

Regarding the key issue, I assume your Prius is equipped with the Smart key system.
To verify, the Toyota emblem on the backside of the key fobs are chrome, there is a black square button on each of the front door outside handles and on the liftgate, and there is a "KEY" button at the bottom of the instrument panel, below the steering column.

Normally, the button would be in the OUT position, enabling the Smart key functions.
Pushing the button IN disables the Smart key and requires using the lock/unlock buttons on the fob and to insert the key fob into the dash slot to start the car.

If there is another smart key somewhere inside the vehicle, it can be started.

To check, have your smart key with you, close all the doors and liftgate, and try to lock the car by pressing the black button on the front door outside handle. If there is another smart key inside the car, it will sound a prolonged beep and not lock. You will still be able to lock the car using the lock button on the key fob.

 

congrats! the key is SUPPOSED to unlock the car and start it, no worries. all the best!

 

Not with the key still inside the house.

 

remote start?

 

Maybe... but then would the OP consider that "a funny issue"?
Lets hear from the OP.

 

What's wrong with the AC? Where do you live? The AC is pretty much essential to keeping the battery cool in warmer temperatures.

 

I guess I'm missing the problem here.

 

Congrats on your new Prius! =)

 

Congrats