Commercial fire escape masks (FEMs) use packed bed filters to remove gaseous and vaporous toxic components in the event of building fires. Packed bed filters incur a high pressure drop and commercial masks have no method to remove environmental (fire) or process (reaction and adsorption) heats. Here we derive a computationally efficient numeric model based on a bi-linear driving force (LDF) model to investigate the purification of gas streams in a square channelled monolith filter containing an impregnated activated carbon (AC) section to adsorb and react toxic components, and a section consisting of shape stable phase change materials (SS-PCMs) to absorb heat. The modelled test gas mixture contained an adsorbing component, cyclohexane, and a reacting component, carbon monoxide, permitting the combined effects of heat generation, heat absorption, component reaction and component adsorption to be studied for a novel filter. The bi-LDF model was validated against a three-dimensional model and provided excellent accuracy at significantly reduced computational time ca. 99.7%. Additionally, the bi-LDF model was used to optimise the dimensions and configuration of the filter, specifically finding an optimal channel diameter, 𝑑𝑐ℎ, to wall thickness, 𝑡𝑤, aspect ratio of 𝑑𝑐ℎ = 1.3𝑡𝑤. The optimal configuration consisted of an initial 2.0 cm long mpregnated AC section followed by a 2.5 cm SS-PCM section at the outlet, providing 18 min of thermal protection whilst preventing cyclohexane vapour breakthrough for 21 min. Pt/TiO2 was confirmed to be a viable CO oxidation catalyst with a minimum weight fraction within the impregnated monolith of 2.5 wt%. The success of this work represents a step change in FEM design and more widely in air purification devices where heat absorption is important.