  Effective critical exponents for the \lambda \phi^4 scalar field theory are
calculated as a function of the renormalization group block size k_o^{-1} and
inverse critical temperature \beta_c. Exact renormalization group equations are
presented up to first order in the derivative expansion and numerical solutions
are obtained with and without polynomial expansion of the blocked potential.
For a finite temperature system in d dimensions, it is shown that \bar\beta_c =
\beta_c k_o determines whether the d-dimensional (\bar\beta_c << 1) or
(d+1)-dimensional (\bar\beta_c >> 1) fixed point governs the phase transition.
The validity of a polynomial expansion of the blocked potential near
criticality is also addressed.
