The recently developed method to detect the stress-cracking and crack healing of glasses in real-time （called the RMS-CH in short，Wu et al.，Appl. Phys. Lett. 92，011918-1（2008）） is applied to the detections of crystals. The experimental results of dimethyl phthalate crystal indicate that，under the condition of constant heating rate：1） the crack-healing rate shows a sharp peak as a function of temperature，the peak temperature can be taken as the characteristic temperature Tcch of the crack-healing ，and Tcch=206 K；2） the peak is not symmetric，and the low temperature side is wider than the high temperature side，which means that the crack-healing has started at lower temperatures and the amount of healing below Tcch is more than that above Tcch. This behavior is similar to that in glasses，but Tcch is higher than that of glassy state. Moreover，Tcch is much lower than the melting point of the crystal，which indicates that the crack-healing mechanism is quite different from that of recrystallization. We would like to point out that two dynamical loss peaks related to the crack-healing process are observed for the first time，which will be helpful to the understanding of the mechanisms. The above results also show the feasibility and validity of the RMS-CH method to investigate the stress-cracking and crack-healing in crystals as in glasses.