The problem of thermal grooving was first proposed by Mullins in 1957. Mullins considered the morphological evolution of thin solid surfaces, namely solid films, and focused primarily on the exterior surface motion with surface diffusion as the dominant mass transport process. By assuming a small slope approximation, the problem can be reduced to a linear surface diffusion problem. Mullins showed that there exist self-similar solutions for the linearized problem. In the present study, we prove the existence and uniqueness of a self-similar solution for the original nonlinear Mullins’ problem for sufficiently small values of the contact angle β. We do so by studying a reduced linear ODE system, which allows us to understand the asymptotic behavior of the solutions for the corresponding linear homogeneous operator, and then we prove existence of a unique solution to the nonlinear problem in closed form by iterations in an appropriate Banach space.