This study aims at characterizing ignition of solid targets exposed to spreading fire fronts. In order to model radiant heat fluxes on targets in a realistic way, polynomial heat fluxes are chosen. Analytical solutions for the solid surface temperature evolution regarding different time-varying heat fluxes are discussed for high thermal inertia solids using a mathematical formalism, which allows for the methodology to be extended to the case of low thermal inertia. This formulation also allows calculation of ignition times for more realistic time-dependent fluxes than previous studies on the topic, providing a more general solution to the problem of solid material ignition. Polynomial coefficients are then obtained fitting heat flux coming from absorbing–emitting flames. A characterization of solid material ignition times regarding fire front rate of spread (ROS) is finally performed, showing the need to accurately model heat flux variations in ignition time calculations.