You mentioned a cup of milk so all the thermal energy goes to increase the kinetic energy of the particles. That is the average speed increases and the simple kinetic theory says there is not particle interaction.
If youv had mentioned a solid then it would be slightly more complicated as the thermal energy is carried as vibrational energy, which is a constant exchange between kinetic and potential energy. So if the KE increases then so must the PE, though not at the same time.
You could argue that as it is heated the milk will expand and so the top of the milk will rise higher in the cup and so will have increased potential energy.
But this effect is trivial and usually ignored.
That's why most of the exercises I did at my level would assume that the thermal expansion for liquid/solid is neglected, or the gas is heated in a rigid container to avoid the complexity of the matter