Adherence to fire safety regulations for wood is one of the most important tasks in its use in structural and architectural applications. This article deals with determining the influence of heat flux on the ignition process of spruce (Picea abies L. Karst.) and beech wood (Fagus sylvatica L.). The heat flux was generated by an electric radiant panel. The analysed parameters included the ignition time of the spruce and beech wood samples, the influence of wood density, and sample moisture, and the course of sample combustion, both with and without flame, was observed. The heat flux was maintained at constant values, depending on the distance of the examined sample from the panel, along with the specific power of the radiation panel. The power of the radiation panel was set to constant values of 5 kW and 10 kW. The samples were placed at distances of 50, 70, 100, 150, and 200 mm from the heat source, and heat fluxes in the range of 13–92 kW·m−2 were observed. At a power of 5 kW and a heat flux of 64 kW·m−2, neither the sample of beech nor that of spruce wood, placed at the distance of 100 mm from the radiation panel, exhibited flaming combustion. The ignition time for the beech wood was approximately twice that of the spruce wood, likely due to the higher average wood density. It can be stated that wood density, as one of the main factors, significantly influences the ignition phase of burning. The statistical analysis examined variables including wood type, radiant panel output, distance, and heat flux in relation to ignition time. The analysis revealed a significant difference between ignition time and distance (p-value = 0.0000, H = 37.51583) as well as between ignition time and heat flux (p-value = 0.0000, H = 37.69726). Similarly, the time to ignition for all tested beech wood samples was longer than for spruce wood.