The population density of cities has been increasing with time and the development of industry. Building fires in large cities with high population density cause extensive human and property damage. To prevent such damage, the characteristics of flames such as the thermal radiation and intensity of the fire source must be considered when designing building structures. However, the consideration of these factors is practically inadequate. Accordingly, in this study, when a mattress was ignited in an open environment at a different installation height (0–515 mm), the measurements from a heat flux meter and the calculated thermal radiation were compared, and a comparative analysis was conducted using the existing prediction formulas by researchers described in ISO 24678-7. We examined the fire risk of mattresses according to the mattress installation height. As a result, the fire risk of the mattress was confirmed according to the mattress installation height; upon comparing the experimental and calculated values for radiant heat, it was found to be necessary to estimate the radiant heat using a calculation method that applies the configuration factor differently depending on the change in the flame shape. In addition, as a result of substituting the experimental value into the calculation method of ISO 24678-7 (a method for estimating the radiant heat of liquid combustibles), the experimental value and the calculated value were found to be significantly different. Therefore, similar to ISO 24678-7 for the radiation heat estimation method for “liquid combustibles”, an international standard for establishing the radiation heat estimation method for “solid combustible materials” as a standard was also required for a reasonable analysis of the fire safety phenomenon of solid materials, such as bed mattresses.