A diode-pumped microchip laser containing a quasi-monolithic plano-plano cavity is realized on the basis of a Tm:KLu(WO₄)₂ crystal. The maximum CW output power is 3.2 W (at an absorbed pump power of 6.8 W) and the slope efficiency as high as 50.4%. The laser is operating at 1946 nm in the TEM₀₀ mode with a M²<1.05. Microchip operation with Tm:KLu(WO₄)₂ is, in principle, due to a special crystal cut along the N(g) optical indicatrix axis. This crystal cut possesses positive near-spherical thermal lens that provides the required mode stabilization in the plano-plano cavity. Sensitivity factors of the thermal lens, "generalized" thermo-optic coefficients and constants describing the photoelastic effect are determined for the monolithic Tm:KLu(WO₄)₂ crystal.