Thermoelectric wine coolers are designed to sit on the floor or smaller units can sit on a tabletop/counter top, they should never be built in or integrated to any cabinetry of any kind.  

This type of unit is the most sensitive to changes in ambient temperatures as they cool via a cooling cell which effectively disperses heat from one side of the cell to the other. 

A minimum of 5-10 inches should be left around all of the sides with this type of wine cooler as they do not have the same cooling components as a compressor driven wine cooler.

By boxing in a thermoelectric wine cooler, the ambient temperature will rise. This will cause strain on the internal components and will lead to failure.  This will also void the manufacturers warranty.

Here is an example of how to install a thermoelectric wine cooler: 

Thermoelectric Wine Cooler