Final answer:
The final temperature after heat transfer between two objects will be affected by changes in the mass of the warmer object and by changes in the composition of either object due to the influence of mass and specific heat capacity on heat transfer.
Step-by-step explanation:
When two objects of similar composition but at different temperatures come into contact and reach thermal equilibrium, changes in the mass of one object can indeed affect the final temperature. Considering the principles of heat transfer, if you increase the mass of the warmer object and keep the cooler object the same, the final temperature will be higher than in the initial experiment because the larger mass has more thermal energy to exchange.
Changing the composition of one of the objects will also affect the final temperature after heat transfer. Different materials have different specific heat capacities, which means they require different amounts of energy to change their temperatures. If you change the composition of one of the objects, the final temperature will change because the rate at which the object gains or loses heat, as well as the amount of heat required to change its temperature, will be different.
In regard to the example provided, transferring 1.00 kcal of heat into 1.00 kg of different substances initially at 20.0°C will result in different temperature changes for each substance due to the differing specific heat capacities of water, concrete, steel, and mercury.