The article examines the consequence of thermal buoyancy-driven cross-flow and heat transfer for shear-thinning power-law fluids on the tandem orientation of two cylinders. Finite volume methodology is used to investigate the effect of the gap ratio (2.5 ≤ S/D ≤ 5.5), power-law index (0.2 ≤ n ≤ 1), and Richardson number (0 ≤ Ri ≤ 1) on flow and thermal output parameters at Reynolds number Re = 100 and Prandtl number Pr = 50 in a confined channel. An unprecedented jump has been witnessed in the flow/thermal parameters at the critical gap ratio (critical spacing). At forced convection (Ri = 0), this critical spacing keeps on increasing with shear-thinning character, from S/D = 3.9 (at n = 1) to 4.9 (at n = 0.2). On the contrary, an increase in shear-thinning characteristic leads to a decrease in critical spacing from S/D = 3.9 (at n = 1) to 2.8 (at n = 0.4) for Ri = 1 (mixed convection). The heat transfer rate increases with shear-thinning behavior, with a maximum heat transfer, noted at n = 0.2. A higher unprecedented increment for flow/thermal parameters is seen at critical spacing for the downstream cylinder than the upstream cylinder. At the highest gap ratio, the output parameters for the upstream cylinder approximate that of an isolated cylinder. The time-variant fluctuations in lift coefficients for a shear-thinning flow in a tandem arrangement provide a new understanding of coshedding and extended body flow regimes.