<p>This study presents a modular, multi-nodal analytical algorithm for conducting early-stage thermal analysis of nadir-pointing CubeSats operating in low Earth orbit (LEO). It introduces a scalable thermal model that estimates temperature evolution across satellite faces and internal components, supporting both steady-state and transient analyses. Although the focus is on two primary variables, time and orbital beta angle, the same framework supports additional parameters such as altitude, material properties and power profiles, enabling sensitivity studies in multiple dimensions. The algorithm is validated through a case study of a 3U CubeSat modelled at single-node, six-node and multi-node resolutions. The study revealed critical thermal zones and operational limits under specified conditions, identifying key nodes susceptible to thermal extremes and providing quantitative bounds for operational temperature ranges. The model convergence across orbital cycles was demonstrated, and consistent thermal behaviour was confirmed once equilibrium was reached. This analytical framework bridges the gap between rough thermal estimates and complex numerical simulations, offering a valuable decision-support tool for thermal control system design in small satellite missions.</p>