The Constructal Law states that flow systems evolve to maximize flow access under constraints. This principle has been applied theoretically to Earth's climate system, modeling it as a heat engine that maximizes poleward energy transport. Here we present the first computational implementation of a Constructal climate model, incorporating separate zonal albedo and greenhouse parameters derived from satellite observations. The model divides Earth into tropical "hot" and polar "cold" zones, with energy flow q between them maximized according to Constructal principles. Using a dual-optimization numerical approach, we solve for optimal zone temperatures, boundary latitude, and heat flux. Validation against 24 years of CERES satellite data demonstrates remarkable agreement: modeled zonal temperatures match observations within 1 °C, hot zone area predictions agree within 1%, and interannual variability is accurately captured. The model achieves this performance with minimal parameterization-requiring only solar constant, albedo, greenhouse factors, one tuned conductance parameter, and a tuned oceanic absorption parameter. Results indicate an equilibrium climate sensitivity of approximately 1.1 °C per doubling of CO2, representing a maximum estimate before inclusion of thermoregulatory feedbacks. This ultra-simple spherical model with no explicit ocean or land features successfully reproduces observed temperatures, hot area fraction, and power flow, suggesting current climate models may benefit from incorporating Constructal principles. The success of this first computational Constructal climate model demonstrates that organizing principles based on flow optimization can capture fundamental climate dynamics with unprecedented parsimony.