Abstract: This paper conducts a numerical study on the initial-boundary value problem for a two-dimensional heat equation with concentrated capacity. The paper first transforms the original problem into an inner interface model, which consists of inner interface matching (IIM) conditions at singular points and the standard heat equation at non-singular points. Then, a new discretization method is introduced for the IIM conditions, achieving second-order accuracy, and the second-order finite difference method is used to discretize the heat equation at non-singular points. The new numerical method allows for the selection of different grid step sizes in different subdomains while ensuring accuracy, thus guaranteeing that the singular points fall exactly on the grid nodes. Subsequently, the unique solvability of the numerical method and the unconditional optimal error estimate in the discrete H¹ norm are analyzed. Finally, numerical results are carried out to verify the effectiveness of the proposed method.