A closed-form analytical solution for temperature distribution in a rectangular slot structure is presented. The methodology models windings, lamination and slot insulation as three distinct regions and formulates a boundary value problem for each region. The solutions follow Poisson's and Laplace's equations. The closed-form nature of the solution allows it to be used for electric machine design and protection. The model is compared with a lumped parameter model, and verified using three-dimensional finite element analysis (FEA) and experimental measurements on a linear induction machine. Slot temperature predictions using the proposed model are within 3.2% of FEA. Model temperature estimates in the slot, lamination, and end winding are all within 6.7% of experimental measurements. This temperature estimation accuracy suggests that the proposed approach is suitable for applications where fast and flexible thermal modeling is necessary.