When a cool object is placed in direct contact with a warm object , describe the flow of energy

All forms of energy tend to flow from place of higher concentration towards the lower concentration. A cool object is at lower energy and a heated object is at higher energy state.

When two objects at different temperatures will be brought into contact, the energy (in form of heat) will flow from body at high temperature(warm object) towards the body at low temperature(cool object) till the point both objects are at same energy level and hence the same temperature.