  Low temperature specific heat (SH) has been measured in K$_x$Fe$_{2-y}$Se$_2$
single crystals with T$_c$ = 32 K. The SH anomaly associated with the
superconducting transition is moderate and sharp yielding a value of $\Delta
C/T \mid_{T_c}$ = 11.6 $\pm$ 1.0 $mJ/mol K^2$. The residual SH coefficient
$\gamma(0)$ in the superconducting state at T$\rightarrow$ 0 is very small with
a value of about 0.39 $mJ/mol K^2$. The magnetic field induced enhancement of
the low-T SH exhibits a rough linear feature indicating a nodeless gap. This is
further supported by the scaling based on the s-wave approach of the low-T data
at different magnetic fields. A rough estimate tells that the normal state SH
coefficient $\gamma_n$ is about 6 $\pm$ 0.5 $mJ/mol K^2$ leading to $\Delta
C/\gamma_nT\mid_{T_c}$ = 1.93 and placing this new superconductor in the strong
coupling region.
