Integrated simulations for fast ignition with a cone-guided target and a 10 ps heating laser have been performed to investigate core heating properties in FIREX-I experiments. It is found that the fast electron beam intensity scales well as the inverse square root of the front electron density, and the averaged core temperature reaches a higher value when the preformed plasma on an inner surface of the cone tip has a longer scale length. As the scale length of the preformed plasma is not easily controllable, a low-density foam coated target is proposed to prevent the reduction in the fast electron beam intensity during the laser irradiation. Optimum foam density and thickness are estimated by averaged core electron temperatures calculated by the integrated simulations.