The lattice data for the energy density of $SU(2)$ gauge theory are calculated with \nop~derivatives of the coupling constants. These derivatives are obtained from two sources : i) a parametrization of the \nop~beta function in accord with the measured critical temperature and $\Delta\beta-$values and ii) a \nop~calculation of the presssure. We then perform a detailed finite size scaling analysis of the energy density near $T_c$. It is shown that at the critical temperature the energy density is scaling as a function of $VT^3$ with the corresponding $3d$ Ising model critical exponents. The value of $\epsilon(T_c)/T^4_c$ in the continuum limit is estimated to be 0.256(23). In the high temperature regime the energy density is approaching its weak coupling limit from below, at $T/T_c \approx 2$ it has reached only about $70\%$ of the limit.