While moving to a new home in Boston, a couple stops the car and the woman opens the door and throws a toy ball on the sidewalk so that their tabby cat can chase after it.
He hides behind an urn and observes the house's owner, Mr. Lawrence, a kindly old magician, have a conversation with the various automatons and gizmos he's created for his magic shows, whilst attempting to fix an electrical bulb-headed one named Edison.
The next day, refusing to be left behind, Thunder is incorporated into the "rabbit out of a hat" routine in the magic show performed for some children at a hospital, to much fanfare.
With Lawrence in the hospital with a broken leg, his nephew Daniel takes advantage by tricking his uncle to sign over power of attorney, in the hopes of putting his house up for sale.
Desperate, Thunder gets Carlo and Carla to dive bomb and splatter poop on them to attempt to deter and prevent the house from being sold.
When Lawrence rushes back from the hospital with the help of some of the children he met there and finds his nephew swinging a wrecking ball, he finally discovers Daniel's true colors.
When Lawrence recovers from his injuries, he returns to entertaining children with his magic shows, in which Thunder now has his starring part alongside Jack and Maggie.
Thunder is finally happy to have a family that appreciates him and his Chihuahua friend seeing them all having so much fun attempts to get himself "an audition" to get recruited as part of the team.
In a post-credit scene, Daniel is attempting to convince a new client to sell her house and move to a retirement home but soon learns that she has many, many cats and sneezes violently.
The website's critics consensus reads: "Thunder and the House of Magic lacks real narrative depth, but its visual splendor offers sufficient compensation for younger viewers.