If you just bought a manual miter box, a simple modification will extend its useful service life. Insert and fasten a piece of 1x stock to the inside bottom of the box. The saw blade will then cut into the false bottom, without damaging the miter box itself. Occasionally move the wood back and forth, or turn it over, to spread out the wear. When badly cut up, just replace the piece.
Using the properly sized room air conditioner is important for comfort and efficiency. Buying too large a unit will chill the air without removing humidity, leaving you feeling cold and clammy. Talk to your dealer to determine the right size for your needs.