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 T(c) and rises rapidly above. For temperatures larger than 2T(c) we find a scaling behavior consistent with sigma(s)(T) = (0.136 +/- 0.011)g4(T)T2, where g(T) is the two-loop running coupling constant with a scale parameter determined as LAMBDA(T) = (0.076 +/- 0.013)T(c).