An arrangement is proposed for a four-stroke internal combustion engine to: (a) recover thermal energy from products of combustion during the exhaust stroke; (b) store that energy as sensible heat in a micro-channel regenerator matrix; and (c) transfer the stored heat to compressed fresh charge that flows through the regenerator during the succeeding mechanical cycle. An extra moveable piston that can be locked at preferred positions and a sequence of valve events enable the regenerator to lose heat to the working fluid during one interval of time but gain heat from the fluid during another interval of time. This paper examines whether or not this scheme for in-cylinder regeneration (ICR) improves the cycle thermal efficiency eta(1). Models for various thermodynamic processes in the cycle and treatments for unsteady compressible flow and heat transfer inside the regenerator are developed. Digital simulations of the cycle are made. Compared to an idealized engine cycle devoid of regeneration, provisions for ICR seem to deteriorate the thermal efficiency. In an 8:1 compression ratio octane engine simulated with an equivalence ratio of 0.75, eta(1) = 0.455 with regeneration and eta(1) = 0.491 without. This study shows that previous claims on efficiency gains via ICR, using highly-simplified models, may be misleading. (C) 2015 Elsevier Ltd. All rights reserved.