It is very well known that tungsten is intrinsically brittle at room temperature, and the characterization of its ductile properties by conventional mechanical tests is possible only above the ductile-to-brittle transition temperature (DBTT), i.e. above 500–700 K. However, the design of tungsten-based components often requires the knowledge of constitutive laws below the DBTT. Here, we carried out instrumented hardness measurements in the temperature range of 300–691 K by nano-indentation. The obtained results are used to extend a set of constitutive laws for the plastic deformation of tungsten, developed earlier on the basis of tensile data, which now covers the temperature range of 300–1273 K. The validation of the constitutive laws was realized by the crystal plasticity finite element method (CPFEM) model, which was applied to simulate the nano-indentation loading curves. The distribution of stress and strain under the indenter was also studied by the CPFEM to bring an insight on the extension of the plastic zone in the process of the indentation, which is of crucial importance when nano-indentation is used to resolve the microstructural features generated by e.g. irradiation by energetic particles, plasma exposure or thermo-mechanical treatment.