The cost of including full kinetics in realistic computations remains extremely high. This has led many researchers to develop reduction techniques for the chemistry. These methods are generally valid only in a very limited range of equivalence ratio, pressure, or temperature and require extensive human time to develop the reduced schemes. Recently, an automatic method based on intrinsic low-dimensional manifolds (ILDM) has been proposed. Because of ILDM, the reduction of detailed reaction schemes is much simplified, leading to the fast generation of look-up tables containing the information corresponding to the reduced chemical schemes. Nevertheless, the ILDM method is not well suited to describe the low-temperature domain, since the dimension and therefore the complexity of the databases increase tremendously in this zone. In this work, we propose a new version of the ILDM method, called flame prolongation of ILDM (FPI), which enables us to solve the problem at low temperatures. We used laminar premixed free flames to extend the manifolds generated with ILDM, thus leading to smooth and accurate evolutions of the species along all the flame front. In order to demonstrate the interest of FPI, we computed the response of a premixed flame to straining using the double-premixed counterflow flame configuration. We show that using FPI, the correct evolution is obtained for all species from almost unstrained flames up to flames near extinction. The computational times are tremendously reduced with FPI in comparison with full chemistry.