8.1.4.10 Geometric and physical applications

Problem: The rate of heat loss of a body is proportional to the difference in the temperatures between the body and its environment (Newton's law). Find the dependence of temperature \( T \) at time \( t \), if the body, heated up to \( T_{0} \) degrees, is brought into a room, the temperature in which is constant and equal to \( \alpha \) degrees.