So, if entropy changes with temperature, then why is it in units of J/K*mol?
Do I have to multiply the temperature by the difference in entropy values to obtain J/mol?
The units of entropy are J/K because entropy gives energy per temperature.
The entropy function for simple systems is S=S(U,V,N) where U is internal energy, V is volume, and N is amount of matter.
Moreover, U can be expressed as a function of temperature and substituting back you can find a function S=S(T,V,N)