A pair of metal heat sinks with half-round groove is always used to hold the crystal rod and dissipate heat in solid-state lasers working with round-rod material. The nonuniformly distributing of assembling pressure on the contact surfaces of the crystal rod and heat sinks makes the thermal contact conductance change along the circumference direction, and causes distribution of temperature inside the crystal rod non-axisymmetric. Two methods of using three or four heat sinks to hold the crystal rod are presented. The relationship between thermal contact conductance and assembly pressure is discussed using the truncated-Gaussian model and the plastic-deformation model. Distributions of the temperature inside the crystal are obtained by the finite element method based on the contact heat-dissipating model. The results show that the pressure and the thermal contact conductance on the side-face of the crystal change obviously along the circumference direction when using a pair of metal heat sinks, which reach maximum in the bottoms of the sink grooves and minimum in the joining directions of the surfaces of heat sinks. And the end-face temperature of the crystal changes largely along the circumference direction. In the method of using three heat sinks, the uniformity of pressure, thermal contact conductance and temperature distribution inside the crystal are greatly improved, and central value of the end-face temperature is reduced. When using four heat sinks, the result is the best and the central end-face temperature is the lowest.