Investigating thermal convection within porous media permeated by fluids and micro-organisms stands as a significant inquiry with broad relevance across geophysical and engineering domains. Studying convection within porous media can aid in controlling temperature and nutrient distribution for cell growth and tissue regeneration, as well as the efficiency of biofuel fermentation and production processes. Hence, the primary objective of this study is to investigate the influence of time-periodic gravitational forces on Darcy–Brinkman bio-thermal convection within a porous medium layer. This medium is saturated with a Newtonian fluid that encompasses gyrotactic micro-organisms. The gravity modulation amplitude is assumed to be very small. A weak nonlinear stability analysis is performed to analyze the stationary mode of bioconvection. The heat transport, measured by the Nusselt number, is governed by a non-autonomous Ginzburg–Landau equation. The research explores the influence of several parameters on heat transport, including the Vadaszs number, the modified bioconvective Rayleigh–Darcy number, cell eccentricity, modulation frequency, and modulation amplitude. The results are presented graphically, illustrating the impact of these parameters on heat transfer. The findings reveal that both the Vadaszs number and the modulation amplitude have a positive effect on heat transfer, enhancing the process. On the other hand, an increase in the modified bioconvection Rayleigh–Darcy number and cell eccentricity leads to a decrease in heat transfer. Furthermore, a comparison between the modulated and unmodulated systems indicates that the modulated systems have a more significant influence on the stability problem compared to the unmodulated systems. This highlights the effectiveness of external modulation in controlling heat transport within the system.

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