We show on a few examples of one-band materials with spheroidal Fermi surfaces and anisotropic order parameters that anisotropies γH of the upper critical field and γλ of the London penetration depth depend on temperature, a feature commonly attributed to multiband superconductors. The parameters γH and γλ may have opposite temperature dependences or may change in the same direction depending on the Fermi-surface shape and on the character of the gap nodes. For two-band systems, the behavior of anisotropies is affected by the ratios of bands densities of states, Fermi velocities, anisotropies, and order parameters. We investigate in detail the conditions determining the directions of temperature dependences of the two anisotropy factors.