  We used data from the Helioseismic and Magnetic Imager (HMI), and Atmospheric
Imaging Assembly (AIA) on the \textit{Solar Dynamics Observatory} (SDO) to
study coronal loops at small scales, emerging in the quiet Sun. With HMI
line-of-sight magnetograms, we derive the integrated and unsigned photospheric
magnetic flux at the loop footpoints in the photosphere. These loops are bright
in the EUV channels of AIA. Using the six AIA EUV filters, we construct the
differential emission measure (DEM) in the temperature range $5.7 - 6.5$ in log
$T$ (K) for several hours of observations. The observed DEMs have a peak
distribution around log $T \approx$ 6.3, falling rapidly at higher
temperatures. For log $T <$ 6.3, DEMs are comparable to their peak values
within an order of magnitude. The emission weighted temperature is calculated,
and its time variations are compared with those of magnetic flux. We present
two possibilities for explaining the observed DEMs and temperatures variations.
(a) Assuming the observed loops are comprised of hundred thin strands with
certain radius and length, we tested three time-dependent heating models and
compared the resulting DEMs and temperatures with the observed quantities. This
modeling used Enthalpy-based Thermal Evolution of Loops (EBTEL), a
zero-dimensional (0D) hydrodynamic code. The comparisons suggest that a medium
frequency heating model with a population of different heating amplitudes can
roughly reproduce the observations. (b) We also consider a loop model with
steady heating and non-uniform cross-section of the loop along its length, and
find that this model can also reproduce the observed DEMs, provided the loop
expansion factor $\gamma \sim$ 5 - 10. More observational constraints are
required to better understand the nature of coronal heating in the short
emerging loops on the quiet Sun.
