Off-grid systems have emerged as a sustainable and cost-effective solution for rural electrification. In sub-Sarahan Africa (SSA), a great number of solar-hybrid microgrids have been installed or planned, operating stand-alone or grid-tied to a weak grid. Presence of intermittent energy sources necessitates the provision of energy storage for system balancing. Reliability and economic performance of those rural microgrids strongly depend on specific control strategies. This work develops a predictive control framework dedicated to rural microgrids incorporating a temperature-dependent battery degradation model. Based on a scalable DC PV-battery microgrid, the realistic simulation shows its superior performance in the reliability improvement and cost reduction. Compared with the day-ahead control without the temperature-dependent battery degradation model, this control strategy can improve the reliability by 5.5% and extend the lead-acid battery life time by 26%, equivalent to lowering the levelised cost of electricity (LCOE) by 13%.