Kojak first appeared when he, Benedict, Fenwick, and their men infiltrate a U.S. military base to steal a tractor beam, as part of Benedict's evil plan to send the Earth to a new Ice Age to destroy summer vacation in his effort to raise test scores. After that, they head onward to Third Street Elementary School, which was closed for the summer and Benedict used to be the principal there before his former best friend Peter Prickly replaced him.
As per Benedict's orders, Kojak was assigned to keep the school clear any suspicion of outside authorities, which led him to develop a grudge against T.J. Detweiller (the protagonist of the film) for his suspicions (also for his 'ugly bald guy' comment when he was spying on them). T.J. tried to inform Principal Prickly about this, but Prickly ends up being captured and locked inside the school. To avoid any more suspicions, Benedict had Kojak to pose as Prickly walking outside the school with several of his men.
When T.J. and his friends quietly sneak into the school, they start to investigate until they accidentally blow their cover. The gang manage to escape, except for T.J., who ends up being captured by Kojak, who then locks him up in the stock room with the real Prickly. After releasing Prickly and getting to his office through the vents, T.J. learns of Benedict's plan just before Kojak arrives and locks him and Prickly up again.
Eventually, T.J.'s friends manage to round all students to help reclaim the school, thanks to Gus Griswald's leadership skills. Despite the success, Kojak confronts the kids and is about to get them, but T.J. and Prickly (having freed themselves again) pour a vat of corn chowder on him, sending him to fall down the stairway.
During the final battle between Benedict's men and the combined groups of the students and staff of Third Elementary, Kojak arrives to the scene, having got some corn chowder on his head and suit. Spotting T.J., Kojak angrily attempts to beat him up for the humiliation he caused, but Muriel Finster arrives to the rescue by challenging Kojak to a fist fight. Finding the idea of beating an old lady to be amusing, Kojak accepts and prepares to fight, but he underestimates Finster as she easily punches him down many times before socking him below the jaw, knocking him out for good. T.J. then thanks Finster for saving his life.
It is unknown what happened to Kojak after Benedict was defeated and the tractor beam was destroyed, either he ended up being smothered by the destruction or perhaps was arrested and sent to prison with Benedict and the rest of their men.