The best replacement for specific heat is heat capacity.

The best alternatives to specific heat are rated as following:
★★★★★  heat capacity
★★  latent heat
★★  thermal conductivity
★★  enthalpy
★  calorie
★  molar heat
★  specific heat capacity
★  heat of fusion
★  specific gravity
★  atomic mass
★  sensible heat
★  thermal capacity
  heat of vaporization
  low specific heat
  atomic weight
  heat of combustion
  specific capacity

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Speaking about specific heat, one probably shouldn't forget about calorimeter.

Other search terms related to specific heat and their ratings are:
★★★★★ calorimeter
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