No, heat will not transfer between two objects with the same temperature.
Here's why:
Heat transfer is the flow of thermal energy from a higher-temperature object to a lower-temperature object. This flow occurs because of a temperature difference, which signifies different levels of internal energy or kinetic energy of the particles within the objects.
Temperature is directly related to the average kinetic energy of the particles in an object. Higher temperature indicates faster-moving particles with higher kinetic energy, while lower temperature means slower-moving particles with lower kinetic energy.
When two objects are at the same temperature, their particles have the same average kinetic energy. This means there is no driving force for the net transfer of energy from one object to the other. Any random transfer of energy between individual particles will be balanced by equal and opposite transfers in the other direction, resulting in no net heat flow.
Therefore, even though microscopic energy exchanges might happen, there will be no overall heat transfer between two objects with the same temperature.
In summary:
Temperature difference drives heat transfer, not just contact.
Same temperature means equal average kinetic energy of particles, preventing net heat flow.
Individual energy exchanges may occur, but they cancel out in both directions.