<p>Fins are essential components in many thermal management systems due to their flexible geometry and high efficiency in heat transfer. They are used in applications such as electronic devices, nuclear reactor cooling, and solar energy systems. Among various fin shapes, pyramidal spine fins received attention because of their capacity to improve CPU heat sink performance. Motivated by these applications, the present study investigated the thermal characteristics of an inclined pyramidal spine fin subject to a convective-radiative environment. Additionally, the spine is considered a porous surface, and its interaction with the surrounding fluid is demonstrated using Darcy’s model. By introducing suitable non-dimensional terms, the governing heat equation is transformed into a dimensionless ordinary differential equation (ODE). The resultant equation was solved semi-analytically using a shifted Vieta-Pell polynomial collocation method (SVP-PCM). The novel SVP-PCM approach is distinguished by its close agreement with results from known numerical techniques, showing its robustness and reliability when compared with existing data. Key thermal parameters and their effects are shown graphically. The outcomes reveal that the enhancing values of radiation parameter (from 0 to 3) and convection-conduction parameter (from 2 to 4) improve heat transmission efficiency by 29.82% and 69.28% respectively. Conversely, an increase in the ambient temperature parameter (from 0.2 to 0.5) leads to a decrement of heat transfer rate by 37.5%.</p>