  Using quantitative perturbation theory for linear operators, we prove
spectral gap for transfer operators of various families of intermittent maps
with almost constant potentials ("high-temperature" regime). H\"older and
bounded p-variation potentials are treated, in each case under a suitable
assumption on the map, but the method should apply more generally. It is
notably proved that for any Pommeau-Manneville map, any potential with
Lispchitz constant less than 0.0014 has a transfer operator acting on Lip([0,
1]) with a spectral gap; and that for any 2-to-1 unimodal map, any potential
with total variation less than 0.0069 has a transfer operator acting on BV([0,
1]) with a spectral gap. We also prove under quite general hypotheses that the
classical definition of spectral gap coincides with the formally stronger one
used in (Giulietti et al. 2015), allowing all results there to be applied under
the high temperature bounds proved here: analyticity of pressure and
equilibrium states, central limit theorem, etc.
