In this article, with the help of a mapping with the involution property, the concept of a nonlocal analogue of the Laplace operator is introduced. For the corresponding nonlocal parabolic equation in a cylindrical domain, the solvability of some inverse problems is studied. Two types of inverse problems of finding the right side of the equation are considered. In the first problem, in addition to solving the equation, a factor is sought that depends on the spatial variable. And the second task is devoted to finding a function that depends on a temporary variable. In the study of these problems, the essential properties of the eigenfunctions of the spectral problem for a nonlocal Laplace operator with a Dirichlet-type boundary condition are used. These properties of eigenfunctions make it possible to apply the Fourier variable separation method to finding solutions to the problems under consideration. The solution of the first problem is in the form of a series expanded in terms of eigenfunctions. When solving the second problem, the theory of Volterra integral equations of the second kind is used. Theorems on the existence and uniqueness of solutions of the problems under consideration are proved.