Thermal analysis of the monoclinic solid state laser host KLu(WO4)2 is presented. The specific heat was measured by the relaxation method in the temperature range from 1.9 to 385 K: its value at room temperature is 0.324 J/gK. The Debye temperature and the sound velocity amount to 303+/-3 K and 3734 m/s. The linear thermal expansion tensor was measured by X-ray powder diffraction from room temperature up to 773 K. The eigenvalues of this tensor are alpha'(11)=8.98 x 10(-6) K(-1), alpha'(22)=3.35 x 10(-6) K(-1), and alpha'(33)=16.72 x 10(-6) K(-1), with the maximum value in the a-b crystallographic plane, at 31.94 degrees from the N(g) principal optical axis. The thermal diffusivity and its anisotropy in the temperature range between 300 and 500 K were measured by the pyroelectric method to determine the thermal conductivity tensor. The eigenvalues of the thermal conductivity are kappa'(11)=2.95 Wm(-1)K(-1), kappa'(22)=2.36 Wm-1K-1, and kappa'(33)=4.06 Wm(-1)K(-1), with the maximum value along a direction again in the a-b crystallographic plane, at 40.75 degrees from the N(g) principal optical axis. Simulation of the temperature distribution in a bulk sample of KLu(WO4)2 with dimensions 3 x 3 x 3 mm(3) shows that pump and laser beam directions along the N(p) principal optical axis in terms of thermal effects are preferable because the propagation is along a quasi-isothermal path.