As for the "breaks", don't bluntly stop : keep running at a slower pace until you reach again your breath -- you can slow down to a walking pace, even drinking and eating, but
do not stop.
Or else, blood goes down :
- You're hot, so skin's veins are dilated, it lower the blood pressure so blood go back slower to the heart.
- You're tired, so your veins struggle to send back the blood to the heart (that's why we have dark rings under the eyes).
- Plain muscles are a part of the blood circulation engine, too (that's why when people are confined to bed for long time they're given anticoagulants).