The beam heat load and the pressure in the vacuum chamber of the cold bore superconducting undulator installed at ANKA (ANgstrom source KArlsruhe) have been monitored for almost two years. Possible sources of the observed heat load could be synchrotron radiation from upstream magnets, image currents, electron and ion bombardment. In this paper, the various possible contributions to the heat load are discussed and compared with experimental results. The dynamic pressure increases nonlinearly with the average beam current. The current where it assumes a maximum varies both with the bunch intensity and with the initial vacuum pressure. A correlation between the heat load and the dynamic pressure has been observed. This study suggests that electron bombardment could explain the beam heat load and pressure rise observed for a bunch length of 10 mm.