What part of the brain deals with short term memory

I believe it is the Medial Temperal Lobe. It is part of the brain known as the limbic system, which includes the hippocampus, the amygdala, the cingulate gyrus, the thalamus, the hypothalamus, the epithalamus, the mammillary body and other organs, many of which are of particular relevance to the processing of memory.

The prefrontal cortext is the place that is responsible for short term memory.