Sure the temperature dependence is crucial and extremely complicated, but not to spontaneously gather enormous MeV-scale energy for crossing the Coulomb barrier or n + p -> n, only because this temperature mostly translates into average energy and so statistics of trajectories of the only player which could really help here: electron.
In Gryzinski's book (page 163 of "Sprawa atomu") he writes that his model expects that pp fusion in the core of a star should be reduced with rise of temperature, and that paper of Eganova confirms it, but I couldn't find it.
"The problem is, the LENR often produces no gamma, not to say in "cylindrically symmetric EM impulses" (WTF is it supposed to mean? - no dipole antenna would produce such a shape of EM signal). Instead of it, whole the energy gets absorbed and thermalized inside the lattice - which is impossible to explain, if we insist that "it practically doesn't matter if atoms are in crystal or amorphous"."
Cylindrical symmetric EM wave is produced e.g. by accelerated charges in linear antenna - pulsating dipole, which doesn't have emphasized any direction perpendicular to the axis
http://ocw.upm.es/teoria-de-la…nnas_athens09_tuesday.pdf
While photon maintains its localized energy for a long distance, cylindrical wave losses energy density e.g. like 1/r.
Hence such energy from pep collapse would be quickly dispersed, caught mainly by millions of electrons - indeed locally raising temperature.
Here are some modes from the linked presentation about linear antennas - arrow around axis denotes cylindrical symmetry: