The total momentum before and after the collision must be conserved.
The total momentum before the collision is:

where m1 and m2 are the masses of the two players, and

and

their initial velocities. Both are considered with positive sign, because the two players are running toward the same direction.
The final momentum is instead

because now the two players are moving together with a total mass of (m1+m2) and final speed vf.
By requiring that the momentum is conserved

we can calculate vf, the post-collision speed:


and the direction is the same as the direction of the players before the collision.
Answer:
This does not violate the conservation of energy.
Explanation:
This does not violate the conservation of energy because the hot body gives energy in the form of heat to the colder body, this second absorbs energy. This will be the case until both bodies reach the same temperature, reaching thermal equilibrium and reducing the transfer of thermal energy. In this way the energy was only transferred from one body to another but the total energy of the system (body 1 plus body 2) will be the same as in the beginning, respecting the principle of conservation of energy or also called the first principle of thermodynamics .
The part of physics that studies these processes is in turn called heat transfer or heat transfer or thermal transfer. Heat transfer occurs whenever there is a thermal gradient or when two systems with different temperatures come into contact. The process persists until thermal equilibrium is reached, that is, until temperatures are equalized. When there is a temperature difference between two objects or regions close enough, the heat transfer cannot be stopped, it can only be slowed down.