The conceptual design of a helium-cooled solid breeder blanket for a moderate sized tokamak fusion reactor is presented to explore the feasibility of heat extraction for power conversion. A compact reactor is considered with a major radius of 3 m, fusion power of 200 MW, and modular blankets. A configuration of radially stacked breeder units with a nested C-shaped helium flow scheme that enables nearly uniform high temperatures of the helium outlet is proposed. A detailed thermal analysis of the central module of the blanket is presented. A model is developed to carry out the one-dimensional thermal transient analysis of the breeder unit, which is benchmarked with ANSYS simulation. This can be used as a tool for rapid scan of the conceptual design for a wide range of parameters. The calculations show that a minimum pulse length of 2000s or above is required to achieve a steady-state blanket temperature for efficient heat extraction.