If two objects have different temperatures when they come in contact, heat will flow from the warmer object to the cooler one UNTIL

They both have an equal temperature.

Explanation:

Any material or object that allow the conduction (transfer) of electric charge or thermal energy is generally referred to as a conductor. Some examples of a conductor are metals, copper, aluminum, graphite, etc.

In the process of heat conduction, thermal energy is usually transferred from fast moving particles to slow moving particles during the collision of these particles. Also, thermal energy is typically transferred between objects that has different degrees of temperature and materials (particles) that are directly in contact with each other but differ in their ability to accept or give up electrons.

Hence, if two objects have different temperatures when they come in contact, heat will flow from the warmer object to the cooler one until they both have an equal temperature.