When one object heats another, does the temperature increase of one object always equal the temperature decrease of the other object?

The change in temperature of the two objects can only be the same when said objects have the same specific heat value.

Specific heat is the amount of energy required to raise 1 gram of substance by 1 degree Celsius. It is also the energy required to lower 1 gram of substance by 1 degree Celsius.

Knowing this, if a substance 1 with a specific heat value of #x# gives #y# energy away to substance 2, which has a specific heat value of #z#, then the energy gained will still be #y#, but since substance 2 requires more/less energy to change temperature than substance 1, the change in temperature is different.

Example Liquid water has a specific heat value of 4.18 joules per gram by degree Celsius. Ice has a specific heat value of 2.10 joules per gram by degree Celsius. If the water gave away 4.18 joules of energy to the ice, the water's temperature would go down by 1 degree Celsius, whilst the ice's temperature increases by about 2 degrees Celsius. The ice gained the same amount of energy as the water lost, but the change in temperature was different.