It heats up because it's consuming/manipulating current.
Even though the adapter isn't in use, it's technically powered up.
Without going too deep into electronics engineering, it's important to remember that the USB port is supplying a minimum of 5V. Most USB-to-Ethernet controller chips operate at 3.3V (i.e. Microchip LAN9500A controller)
The factors that would create heat are basically twofold:
- Reduction of the voltage to 3.3 volts
- Powering the chip
To reduce the voltage, manufacturers use one of two components - linear regulators or buck converters. Linear regulators, which are quite cheap compared to buck converters reduce power through the dissipation of heat. Buck converters on the other hand, are extremely efficient (meaning the run cooler) but more costly. In low voltage scenarios, it's not uncommon to find linear regulators since the tolerances are so generous.
Powering the chip
Looking at the specifications page, the chip referenced above uses 395mW (.4W) in "low power" or "Suspend0" mode. Keep in mind, the device manufacturer may not implement these low power features for cost savings.
When it's transmitting (sending data) it uses 692mW (.7W) of power.
In terms of heat transfer, 1W per second = 1 Joule. Where a Joule = "The heat required to raise the temperature of 1g of water by 0.24 °C"
Between the chip transmitting/receiving ethernet packets as well as converting ethernet to USB as well as the heat generated by reduction of the voltage it's supplied, it's not surprising the adapter can appear "hot" especially if the manufacturer uses less efficient components for cost savings.