Ordinary chondrite meteorites contain silicates, Fe,Ni-metal grains, and troilite (FeS). Conjoined metal-troilite grains would be the first phase to melt during radiogenic heating in the parent body, if temperatures reached over approximately 910-960 degrees C (the Fe,Ni-FeS eutectic). On the basis of two-pyroxene thermometry of 13 ordinary chondrites, we argue that peak temperatures in some type 6 chondrites exceeded the Fe,Ni-FeS eutectic and thus conjoined metal-troilite grains would have begun to melt. Melting reactions consume energy, so thermal models were constructed to investigate the effect of melting on the thermal history of the H, L, and LL parent asteroids. We constrained the models by finding the proportions of conjoined metal-troilite grains in ordinary chondrites using high-resolution X-ray computed tomography. The models show that metal-troilite melting causes thermal buffering and inhibits the onset of silicate melting. Compared with models that ignore the effect of melting, our models predict longer cooling histories for the asteroids and accretion times that are earlier by 61, 124, or 113kyr for the H, L, and LL asteroids, respectively. Because the Ni/Fe ratio of the metal and the bulk troilite/metal ratio is higher in L and LL chondrites than H chondrites, thermal buffering has the greatest effect in models for the L and LL chondrite parent bodies, and least effect for the H chondrite parent. Metal-troilite melting is also relevant to models of primitive achondrite parent bodies, particularly those that underwent only low degrees of silicate partial melting. Thermal models can predict proportions of petrologic types formed within an asteroid, but are systematically different from the statistics of meteorite collections. A sampling bias is interpreted to explain these differences.