If the temperature between two bodies is same, heat transfer will happen between them.
False
If the two bodies in contact have the same temperature then there is no heat transfer between them. So, Given statement is false.
Temperature is defined as the measure of internal vibrational energy of an object. When a given object comes into contact with another with a higher temperature, that is, a higher internal vibrational energy, the energy from latter is transferred to the former until the energy of both the objects is equalized. When two bodies having the same temperature are kept in contact with each other, no such transfer of enegry is possible, hence no flow of heat is witnessed.