We use inelastic neutron scattering to measure the magnetic excitations in underdoped La2-xSrxCuO4 (x=0.085, T_{c}=22 K) for large energy (5<E<200 meV) and temperature (5<T<300 K) ranges. At low T, the response is highly structured in E and q, with peaks in the local susceptibility at 15 and 50 meV and a four-peaked structure in q for E approximately 185 meV. Raising T from 30 K greater, similarT_{c} to 300 K causes the structure in chi;{''}(q,omega) present for E<70 meV to disappear. It is replaced with a strongly damped response. We attribute this change to the disappearance of the pseudogap with increasing temperature.