  We report electric detection of the spin Peltier effect (SPE) in a bilayer
consisting of a Pt film and a Y$_{3}$Fe$_5$O$_{12}$ (YIG) single crystal at the
cryogenic temperature $T$ as low as 2 K based on a RuO$_2$$-$AlO$_x$ on-chip
thermometer film. By means of a reactive co-sputtering technique, we
successfully fabricated RuO$_2$$-$AlO$_x$ films having a large temperature
coefficient of resistance (TCR) of $\sim 100\% ~\textrm{K}^{-1}$ at around
$2~\textrm{K}$. By using the RuO$_2$$-$AlO$_x$ film as an on-chip temperature
sensor for a Pt/YIG device, we observe a SPE-induced temperature change on the
order of sub-$\mu \textrm{K}$, the sign of which is reversed with respect to
the external magnetic field $B$ direction. We found that the SPE signal
gradually decreases and converges to zero by increasing $B$ up to
$10~\textrm{T}$. The result is attributed to the suppression of magnon
excitations due to the Zeeman-gap opening in the magnon dispersion of YIG,
whose energy much exceeds the thermal energy at 2 K.
