This paper considers the development of self-adaptive solution algorithms for nonlinear heat conduction. By reinterpreting the incremental successive substitution and Newton Raphson procedures as methods involving extrapolations bound by open constraint surfaces, specialized closed constraints are developed that significantly improve the efficiency and stability of such schemes. This is achieved by introducing closed ellipsoidal surfaces to control the size of successive iterations. In particular, due to the nature of the ellipsoidal bound employed, the resulting closed constrained incremental successive substitution and Newton Raphson algorithms are self-adaptive, intrinsically stable, as well as far more efficient than the open versions. Because of the generality of the constrained schemes developed, all the various types of non-linearity common to heat transfer can be treated. To demonstrate the new algorithms developed here, benchmark examples are presented and comparisons are made with traditional schemes.