  Among primordial magnetogenesis models, inflation is a prime candidate to
explain the current existence of cosmological magnetic fields. Assuming
conformal invariance to be restored after inflation, their energy density
decreases as radiation during the decelerating eras of the universe, and in
particular during reheating. Without making any assumptions on inflation, on
the magnetogenesis mechanism and on how the reheating proceeded, we show that
requiring large scale magnetic fields to remain subdominant after inflation
gives non-trivial constraints on both the reheating equation of state parameter
and the reheating energy scale. In terms of the so-called reheating parameter,
we find that ln(Rrad) > -10.1 for large scale magnetic fields of the order 5 x
10^(-15) Gauss today. This bound is then compared to those already derived from
Cosmic Microwave Background (CMB) data by assuming a specific inflationary
model. Avoiding magnetic field backreaction is always complementary to CMB and
can give more stringent limits on reheating for all high energy models of
inflation. For instance, a large field matter dominated reheating cannot take
place at an energy scale lower than typically 500 GeV if the magnetic field
strength today is Bo = 5 x 10^(-15) G, this scale going up to 10^(10) GeV if Bo
= 10^(-9) G.
