In this paper we present numerical simulations of heating of a solid copper cylinder by the 440 GeV proton beam delivered by the Super Proton Synchrotron (SPS) at CERN. The beam is made of 288 proton bunches while each bunch comprises of 1.15.10(11) so that the total number of protons in the beam is about 1.3.10(13). The bunch length is 0.5 ns while two neighboring bunches are separated by 25 ns so that the beam duration is 7.2 mu s. Particle intensity distribution in the transverse direction is a Gaussian and the beam can be focused to a spot size with sigma = 0.1 mm-1.0 mm. In this paper we present results using two values of sigma, namely 0.2 mm and 0.5 mm, respectively. The target length is 1.5 m with a radius = 5 cm and is facially irradiated by the beam. The energy deposition code FLUKA and the two-dimensional hydrodynamic code BIG2 are employed using a suitable iteration time to simulate the hydrodynamic and the thermodynamic response of the target. The primary purpose of this work was to design fixed target experiments for the machine protection studies at the HiRadMat (High Radiation Materials) facility at CERN. However this work has shown that large samples of High Energy Density (HED) matter will be generated in such experiments which suggests an additional application of this facility. In the present paper we emphasize the possibility of doing HED physics experiments at the HiRadMat in the future. (c) 2013 Elsevier B.V. All rights reserved.