Two types of different trials were examined experimentally to increase a cleaving velocity in thermal stress cleaving. One is a partial cooling by water mist spray on the propagating crack surface and the other is a preformation of a slightly high-temperature zone by preheating. It is known that when other cleaving conditions are fixed, the cleaving velocity decreases with increase in width of the target object. This characteristic of thermal stress cleaving is often considered as a shortcoming for practical applications. Therefore, improvement of the cleaving efficiency by increasing a cleaving velocity is one of the important issue in the thermal stress cleaving. It was found experimentally that the maximum attainable cleaving velocity was increased from 38 to 55 mm/s when mist cooling was employed in addition to the usual laser beam heating of 10W magnitude for 31 mm width specimen. On the other hand, the most effective preheat technique realized more than 400% increase in the cleaving velocity for 62 mm width specimen. The background why these two types of different approaches both contribute to improve the cleaving velocity was discussed based on the linear elastic fracture mechanics.