Does E+ take into account the fact that specific heat varies with temperature ?

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Yes, the specific heat of outside air and indoor air of zones change over the course of EnergyPlus simulations. If you are modeling HVAC systems, EnergyPlus can provide results for the zone air using the following output variable:

• Output:Variable,*,System Node Specific Heat,hourly; !- HVAC Average [J/kg-K]

You will need to find the name of the zone air node that you are interested in, then replace the "*" in the two examples above with that zone air node name (or whatever specific node in the HVAC system you are interested in). If you are not modeling HVAC systems, then this output variable is not available.

If you don't see a node name in your model for outdoor air, you could use output variables for other outdoor air properties and calculate specific heat using psychrometric equations.

You are correct that if you apply phase change materials you can specify how their specific heat changes with temperature, but that needs the Conduction Finite Difference algorithm. With the default Conduction Transfer Function algorithm the specific heat set in Material objects stays constant over the simulation.