  The temperature dependence of Tan's contact parameter $C$ and its derivatives
for spin gapped quantum magnets are investigated. We use the paradigm of
Bose-Einstein condensation (BEC) to describe the low temperature properties of
quasiparticles in the system known as triplons. Since the number of particles
and the condensate fraction are not fixed we use the $\mu VT$ ensemble to
calculate the thermodynamic quantities. The interactions are treated at the
Hartree-Fock-Bogoliubov approximation level. We obtained the temperature
dependence of $C$ and its derivative with respect to temperature and applied
magnetic field both above and below the critical temperature $T_c$ of the phase
transition from the normal phase to BEC. We have shown that $C$ is regular,
while its derivatives are discontinuous at $T_c$ in accordance with Ehrenfest's
classification of phase transitions. Moreover, we have found a sign change in
$\partial C/\partial T$ close to the critical temperature. As to the quantum
critical point, $C$ and its derivatives are regular as a function of the
control parameter $r$, which induces the quantum phase transition. At very low
temperatures, one may evaluate $C$ simply from the expression $C=m^2\mu^2/{\bar
a}^{4}$, where the only parameter effective mass of quasiparticles should be
estimated. We propose a method for experimentally measuring of Tan's contact
for spin gapped dimerized magnets.
