B

The statement is false because supplying heat to a body does not always result in an increase in temperature, especially during phase changes.
1. When heat is added to a solid at its melting point, it causes the solid to change to a liquid without increasing the temperature. This process is known as latent heat.
2. Similarly, when heat is added to a liquid at its boiling point, it converts the liquid to vapor without a temperature increase.
Therefore, while heat transfer generally raises temperature, it can also lead to phase changes where the temperature remains constant. Hence, the correct answer is B.