Whenever you destroy an obstacle (either through a Giant, Blast or All-Coin Jelly, a Cookie or Pet's ability, or a treasure such as the Burning Heat Infused Jellyco), the Uncooling Teacup will give you about 30,000~35,000 points when fully upgraded. Your Energy will also drain 20% slower.
When paired with General Jujube Cookie, it generates more arrows and increases the points from destroyed obstacles by 20,000, bringing the total up to 50,000~55,000 points.
This pet is a very special gift received by General Jujube Cookie. One well-known story claims that before his tea cools, General Jujube Cookie can quickly destroy every obstacle that lies in his path. But, shhh... the secret to this trick is that this pet is self-heating.