This paper deals with thermal behaviors of solid particles at ignition in attempting to theoretically delineate transition between thermally thick and thin behavior when a solid target is exposed to a radiant heat flux. In order to evaluate classical asymptotic relation accuracy and limiting range, models are developed for finite-depth target in both Cartesian and cylindrical coordinates, allowing to enhance asymptotic relations. Comparison between finite-depth target solutions and asymptotic solutions finally provides a mapping which allows the suited relation for ignition time calculation to be determined, regarding ignition conditions. This mapping then suggests some interesting consequences on forest fuel ignition and fire propagation modeling, since asymptotic models seem to overlap on large regions. (C) 2014 Elsevier Ltd. All rights reserved.