Relation between current, resistance and voltage according to Ohm's law, Joules law of heat and P=IV
Answering about Ohms law: 


  Ohm's law has sometimes been stated as, "for a conductor in a given
  state, the electromotive force is proportional to the current
  produced." That is, that the resistance, the ratio of the applied
  electromotive force (or voltage) to the current, "does not vary with
  the current strength ." The qualifier "in a given state" is usually
  interpreted as meaning "at a constant temperature"


from: https://en.wikipedia.org/wiki/Ohm%27s_law#Temperature_effects

You are right about the change in resistivity due to change in the temperature. The resistivity has a dependency on temperature. Ohm's law hence is primary defined in a given state. At a constant applied voltage, the current would decrease as in case of conductors and the current would increase as in case of semiconductors. Ohm's law is applicable in a given state. hence, the variable temperature will not be considered.   

https://www.askiitians.com/iit-jee-electric-current/temperature-dependence-of-resistivity/