The increased capacity for self-regulation that is seen in middle and late childhood is linked to developmental advances in the:

Brain's prefrontal cortex.

Explanation:

Brain may be defined as one of the most important organ of the body that helps in the control and coordination of the body. Three main divisions of the brain are forebrain, midbrain and hindbrain.

The prefrontal cortex may be defined as the part of brain situated at the frontal lobe. This area of the brain is involved in the planning, thinking and the complex behavior of an individual. This area of brain is also involved in the development of the self esteem.

Thus, the answer is brain's prefrontal cortex.  

exercising at a moderate intensity, and slowly increasing the duration.