We present results of a detailed investigation of the temperature dependence of the spatial string tension in SU(2) gauge theory. We show, for the first time, that the spatial string tension is scaling on the lattice and thus is nonvanishing in the continuum limit. It is temperature independent below Tc and rises rapidly above. For temperatures larger than 2Tc we find a scaling behavior consistent with σs(T)=(0.136±0.011)g4(T)T2, where g(T) is the two-loop running coupling constant with a scale parameter determined as ΛT=(0.076±0.013)Tc.