Chiddler is correct but he/she is talking about heat of fusion/evaporation.
The answer is still the same for specific heat capacities - they do vary between different phases of the same substance. They actually vary with temperature within the same substance but that's rarely significant unless you're heating them to really high temperatures.
What the specific heat capacity will be depends on how many ways a molecule of the substance can absorb energy. In general, the more degrees of freedom a molecule has, the more energy it can absorb before the temperature being risen. That means that typically it will be higher at higher temperatures but that's a very general trend and you can probably find exceptions. The detailed reasons of why and how exactly it changes are more than what you need for MCAT.