  We compute, both explicitly up to next-to-leading order and in a proof by
induction for all loop levels, the critical exponents for thermal
Lorentz-violating O($N$) self-interacting scalar field theory. They are
evaluated in a massless theory renormalized at arbitrary external momenta,
where a reduced number of Feynman diagrams is eeded. The results are presented
and shown to be identical to that found previously in distinct theories
renormalized at different renormalization schemes. At the end we give both
mathematical explanation and physical interpretation for them based on
coordinates redefinition techniques and symmetry ideas, respectively.
