We report temperature-responsive soft composites of semiflexible biopolymer networks (fibrin) containing dispersed microgel colloidal particles of poly(N-isopropylacrylamide) (pNIPAM) that undergo a thermodynamically driven deswelling transition above the lower critical solution temperature. Unlike standard polymer particle composites, decreasing the inclusion volume of the particles (by increasing temperature) is concomitant with a striking increase of the overall elastic stiffness of the composite. We observe such a behavior over a wide composition space. The composite elastic shear modulus reversibly stiffens by up to 10-fold over a small change in temperature from 25 to 35 degrees C. In isolation, the fibrin network and microgel suspension both soften with increased temperature, making the stiffening of the composites particularly significant. We hypothesize that stiffening is caused by the shrinking microgel particles that deform fibrin filaments, and modify the network structure. We develop a phenomenological model that quantifies this hypothesis, and the derived predictions are qualitatively consistent with our experimental data.