Oxygen tends to be deficient in a narrow space or in a microgravity environment where natural convection is suppressed. When a combustible solid is burned in such an environment, smoldering combustion without flame occurs. Since smoldering combustion is often observed in the initial stage of a fire, insights into smoldering combustion help understand fire growth behaviors at an early stage of a fire. This paper presents a numerical model of the smoldering combustion of a thin solid in a narrow channel. The smoldering spread rate and the fingering pattern formed by a instability mechanism are particularly studied. It is found that heat loss has a significant influence on the smoldering behavior. With an increase in heat loss, instability tends to be enhanced, leading to more frequent fingertip splits and local extinction.