Heat Transfer occurs between a hot source to a colder sink. If there is no temperature difference between source and sink no heat transfer will occur.
Heat Transfer will increase with an increase in temperature difference between the hot source and the colder sink. Heat transfer is very similiar to current in a electical circuit where the the temperature difference represents the voltage difference. In an electical circuit no current will flow if there is no difference in the voltage.
Heat transfer can occur in three ways these are conduction, convection and radiation.
Conduction occurs when there is direct contact with the heat source and the heat sink. For example if you grab a cold can of soda, as shown below, the heat from your hand (heat source) will transfer into the can of soda (heat sink).
Convection occurs when there is colder gas (heat sink) that blows by the heat source. The rate of transfer increases with increased velocity of the air.
Radiation transfer occurs when a radiating body (heat source) radiates to a colder sink. The rate of transfer increases with increased temperature differences and a higher emissivity of the colder sink surface.