  We have analyzed the effect of electron-LO phonon interaction in a
double-barrier resonant tunneling structure under a magnetic field {\bf B}
applied parallel to the tunneling current. While the low temperature
anti-crossing phenomenon has already been investigated, here we study the
phonon absorption resonant magnetotunneling at finite temperatures. The
Matsubara technique is used to sum up resonant diagrams of higher orders, and
the result is selfconsistently renormalized. The phonon absorption tunneling
spectrum has been calculated numerically. The result shows that the
phonon-absorption process produces two broad inelastic wings on the main
elastic tunneling peak, the strength of which is sensitive to the resonant
condition, and grows with increasing temperature. The width of the inelastic
wings are proportional to $B^{1/2}$. This is in contrast to the appearance of
anti-crossing in the phonon emission tunneling process. The difference is due
to the fact that the phonon emission is a coherent process, while the
absorption is a typical incoherent process since absorbed real phonons have
random phases.
