With the planned increase of luminosity at CERN for HL-LHC and FCC, instruments for beam quality control must meet new challenges. The current wires, made up of plain carbon fibers and gold-plated tungsten would be damaged due to their interactions with the higher luminosity beams. We are currently testing a new and innovative material, with improved performance: carbon nanotube fibers (CNTF). The HiRadMat (High Radiation for Material) experimental line at the output of the SPS is a user facility which can irradiate fix targets up to 440 GeV/c. CNTF with various diameters were irradiated in HiRadMat with different intensities, later imaged with a SEM microscope and tested for their mechanical properties. In addition, simulations have been carried out with the FLUKA particle physics Monte-Carlo code, in order to better understand the mechanisms and assess the energy deposition from protons at 440 GeV/c in those CNTF wires, depending mainly on their diameters and densities. This could lead to a good estimation of the CNTF temperature during irradiation. In this contribution, we first present the HiRadMat experimental setup and then we discuss the results of our FLUKA simulations.