Physics of nano-contact in metal-oxide-semiconductor field-effect transistors has been attracting interests of many researchers recently. Contacts are conventionally treated as a reservoir in thermal equilibrium, but behavior of contacts in ultra-small devices is still open questions. In this paper, we investigate electron tunneling between a two-dimensional electron gas (2DEG) and Si quantum dots (QDs) using Si-QDs floating gate metal-oxide-semiconductor (MOS) capacitor samples and found unexpected temperature dependence. This unusual tunneling behavior was phenomenologically explained by considering the wave functions of the 2DEG explicitly. The observed temperature dependence of tunneling currents is originated from the non-thermal-equilibrium nature of the 2DEG electrode.