  The intrinsic background count rate of tungsten superconducting
transition-edge sensors (TES) is low, and the calorimeters using these sensors
can resolve the energy of single photons. These facts make the sensors
particularly interesting for the background-limited searches of new processes
and particles. In this contribution, the intrinsic background of a tungsten TES
has been investigated. After excluding other sources (e.g., cosmic muons,
thermal background) relevant for the observed background rate of
$10^{-4}$~s$^{-1}$ for the detection of photons with a wave length of 1064 nm,
we investigate the impact of natural radioactivity. Dedicated measurements
using gamma-emitters mounted outside the cryostat have been used to estimate
the sensitivity of the TES setup for ionizing radiation. We have found that
indeed an increased background can be observed in the presence of the
radioactive sources. After selecting events which populate our signal region
tuned for single photon detection at near-infrared, roughly 0.5% of the events
produced by gamma-rays appear indistinguishable from those due to single
photons with 1064~nm wave length. This ratio is consistent with that observed
for the residual background detected with the TES at a rate of
$10^{-4}$~s$^{-1}$. From this, we conclude that the bulk of the observed
background count-rate in the signal region can be explained by natural
radioactivity.
