Mill engineers aiming to improve the geometry of rolled strip require knowledge of the temperature distribution in the roll. Theoretical evidence shows that the core temperature evolves more slowly than surface temperatures and governs the thermal expansion of the work roll. For practical purposes then, a model that predicts core temperature will allow online prediction and tracking of roll cambers. The present paper builds on previous work in developing rapid models of roll core temperature. A previous model derived using Laplace transforms is improved using a matrix formulation and conversion from an explicit to an implicit time discretisation. The implicit solution is more stable and allows for larger time steps than the explicit formulation or iterative methods used previously. The model has been tested and found to make good qualitative predictions but to underestimate the camber in comparison with actual plant data and a two-dimensional finite difference model.