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Radiation is an important contributor to the energetics of the interstellar medium, yet its transport is difficult to solve numerically. We present a novel approach towards solving radiative transfer of diffuse sources via backwards ray tracing. Here we focus on the radiative transfer of infrared radiation and the radiation pressure on dust. The new module, \textsc{TreeRay/RadPressure}, is an extension to the novel radiative transfer method \textsc{TreeRay} implemented in the grid-based MHD code {\sc Flash}. In \textsc{TreeRay/RadPressure}, every cell and every star particle is a source of infrared radiation. We also describe how gas, dust and radiation are coupled via a chemical network. This allows us to compute the local dust temperature in thermal equilibrium, leading to a significantly improvement over the classical grey approximation. In several tests, we demonstrate that the scheme produces the correct radiative intensities as well as the correct momentum input by radiation pressure. Subsequently, we apply our new scheme to model massive star formation from a collapsing, turbulent core of 150 ${\rm M}_\odot$. We include the effects of both, ionizing and infrared radiation on the dynamics of the core. We find that the newborn massive star prevents fragmentation in its proximity due to radiative heating. Over time, dust and radiation temperature equalize, while the gas temperature can be either warmer due to shock heating or colder due to insufficient dust-gas coupling. Compared to gravity, the effects of radiation pressure are insignificant for the stellar mass on the simulated time scale in this work.