The Lyapunov–Krasovskii functional method is a well-known tool for analyzing stability and robust stability of time-delay systems. An important element of functionals with a prescribed derivative along the solutions of system is the Lyapunov matrix. This paper investigates the one-dimensional heat equation with delay. An explicit form of the Lyapunov–Krasovskii functional with a prescribed derivative is presented. A new representation of the Lyapunov matrix is introduced via an auxiliary function with fewer arguments, along with an explicit formula for its computation.