Crystals of undoped and laser active Yb-doped NaT1-xYbx(WO4)2, T = Y (x = 0, 0.1), Lu (x = 0, 0.1, 0.5), have been grown by the Czochralski (T = Y) or the top seeded solution growth (T = Lu) methods, depending on their melting nature, congruent or incongruent, respectively. From single-crystal X-ray diffraction analysis, the noncentrosymmetric tetragonal space group I4 has been established for all of them. The Na+/T3+ (Yb3+) occupancy factors for 2b and 2d sites show the lowest departure from the random distribution, and thus the largest cationic disorder, in NaLu0.9Yb0.1(WO4)2, namely 0.43/0.57 and 0.56/0.44, respectively. The thermal expansion tensors have been determined up to 973 K for the five crystals; NaLu(WO4)2 with α1=8.2(2) × 10-6 K-1 and α3= 17.3(4) × 10-6 K-1 coefficients has lower anisotropy than NaY(WO4)2 with α1= 8.4(2) × 10-6 K-1 and α3=18.5(4) × 10-6 K-1 coefficients. From the point of view of the thermal steadiness, the evaluation of the Yb-doped laser layer/optically inert substrate la...