Robotic manipulation in space is essential for emerging applications such as debris removal and in-space servicing, assembly, and manufacturing (ISAM). A key requirement for these tasks is the ability to perform precise, contact-rich manipulation under significant uncertainty. In particular, thermal-induced deformation of manipulator links and temperature-dependent encoder bias introduce kinematic parameter errors that significantly degrade end-effector accuracy. Traditional calibration techniques rely on external sensors or dedicated calibration procedures, which can be infeasible or risky in dynamic, space-based operational scenarios. This paper proposes a novel method for kinematic parameter estimation that only requires encoder measurements and binary contact detection. The approach focuses on estimating link thermal deformation strain and joint encoder biases by leveraging information of the contact manifold - the set of relative SE(3) poses at which contact between the manipulator and environment occurs. We present two core contributions: (1) a differentiable, learning-based model of the contact manifold, and (2) an optimization-based algorithm for estimating kinematic parameters from encoder measurements at contact instances. By enabling parameter estimation using only encoder measurements and contact detection, this method provides a robust, interpretable, and data-efficient solution for safe and accurate manipulation in the challenging conditions of space.