Stellar collisions are an important formation channel for blue straggler stars in globular and old open clusters. Hydrodynamical simulations have shown that the remnants of such collisions are out of thermal equilibrium, are not strongly mixed and can rotate very rapidly. Detailed evolution models of collision products are needed to interpret observed blue straggler populations and to use them to probe the dynamical history of a star cluster. We expand on previous studies by presenting an efficient procedure to import the results of detailed collision simulations into a fully implicit stellar evolution code. Our code is able to evolve stellar collision products in a fairly robust manner and allows for a systematic study of their evolution. Using our code we have constructed detailed models of the collisional blue stragglers produced in the $N$-body simulation of M67 performed by Hurley emph{et al.} in 2005. We assume the collisions are head-on and thus ignore the effects of rotation in this paper. Our detailed models are more luminous than normal stars of the same mass and in the same stage of evolution, but cooler than homogeneously mix