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.
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