Can Heat Transfer occur between two bodies with the same temperature but different states only through Latent Heat Transfer? I understand that temperature difference is the driving force for heat transfer but I have been wondering whether there would be any heat transfer, let's say if steam at 100 degree Celsius and water at 100 degree Celsius are passed through the two sides of a Heat Exchanger.
 A: yes it's possible if the states are somehow not reversible(might not be the proper word for that). For example if you have water and air at ambient temperature then water will evaporate as long as the air isnt saturated.
A: I believe the academical answer to your question is no. There is probably a way to justify properly with the second law of thermodynamics, I will think about it and come back later if I find it. 
However, in practise, you might find processe that very much "look like it", like in the example that Manu was giving.
For now, I would like to come back on it, because I think it is a good illustration. Actually, I half-afgree with his point, but I want to stress that even in this case, it will always be a temperature difference that drives the heat flow.
Let us consider liquid water initally at ambient temperature T in an unsaturated atmopshere. If this atmosphere is unsaturated, our system is not in equilibrium. Indeed, even if the water is way below 100 degrees C, it is still above its boiling point at the partial pressure in water contained in the atmosphere.
This means that the water will indeed spontaneously evaporate. So it does need some heat. But actually, it can take it... from itself ! We are in a superheated state (water below its boiling point in the operating conditions), which means that the water can cool down : it takes its own temperature energy to use it as latent heat ! My point is that this evaporation does not need any transfer from outside : everything could happen adiabatically (like the freezing of a supercooled liquid in isolated conditions, but reversed). The decrease in temperature of the water provide its own necessary energy for evaporation.
This being said, of course, the water is in contact with the air, and we can not provide adiabatic conditions. So indeed, as the water starts to evaporate by its own, it decreases a bit in temperature, so it starts pumping heat from the atmosphere thanks to this newly created dT. 
In the end, the process does take heat from the air, and that helps sutain the evaporation. But this process still occurs thanks to temperature gradient. There is no transfer between phases at the same temperature in this situation (it is just that the process naturally causes gradient to appear)
A: From the perspective of thermodynamics, heat is defined as energy transfer due solely to temperature difference. Period. If there is no temperature difference, there is no energy transfer in the form of heat. 
Phase changes may or may not involve heat transfer. For example, water may evaporate in air even though the water and air are at the same temperature. This is a surface phenomenon due to some water molecules at the surface have higher than the average bulk kinetic energy of the liquid allowing them to escape.
However, when they do it is because the there is a temperature difference between the substance undergoing the phase change and something else.   The heat transfer causes a phase change in the substance without changing the temperature of the substance. This heat is referred to as “latent (hidden) heat” because the heat doesn’t increase the temperature of the substance. 
Hope this helps.
