We present a new model for computing hydration free energies by 3D reference interaction site model (3D-RISM) that uses an appropriate initial state of the system (as suggested by Sergiievskyi et al.). The new adjustment to 3D-RISM theory significantly improves hydration free energy predictions for various classes of organic molecules at both ambient and non-ambient temperatures. An extensive benchmarking against experimental data shows that the accuracy of the model is comparable to (much more computationally expensive) molecular dynamics simulations. The calculations can be readily performed with a standard 3D-RISM algorithm. In our work, we used an open source package AmberTools; a script to automate the whole procedure is available on the web (https://github.com/MTS-Strathclyde/ISc).