Infrared heating has been demonstrated as an effective technique to smooth solid hydrogen layers inside transparent cryogenic inertial confinement fusion capsules. Control of the first two Legendre modes of the fuel thickness perturbations using two infrared beams injected into a hohlraum was predicted by modeling and experimentally demonstrated. In the current work, we use coupled ray tracing and heat transfer simulations to explore a wider range of control of long scale length asymmetries. We demonstrate several scenarios to control the first four Legendre modes in the fuel layer using four beams. With such a system, it appears possible to smooth both short and long scale length fuel thickness variations in transparent indirect drive inertial confinement fusion targets