(Note that while your textbook explains in detail what thermal internal energy is, it does not actually define a symbol for thermal internal energy, so for our purposes we'll use "Etherm.")
Instead of finding out how much thermal internal energy Etherm an object has, often we are more concerned with its initial-to-final change ∆Etherm, which is the final amount of thermal internal energy minus the initial amount of thermal internal energy. Notice how the common factors of mass m and specific heat capacity c are pulled out, such that the amount of change in thermal internal energy is determined by the ∆T change in temperature.
During vaporization (liquid turning into gas) or melting (solid turning into liquid), these bonds are broken, freeing up individual atoms or molecules. Bond internal energy increases during these processes, much like the elastic potential energy of a spring increasing as it stretches more and more, because the bonds between atoms and molecules must be stretched further apart in order to "disconnect" them from each other.
During condensation (gas turning into liquid) or freezing (liquid turning into solid) bonds begin to form between the individual atoms or molecules. Bond internal energy decreases during these processes, much like the elastic potential energy of a spring decreasing as it stretches less, because the distances between atoms and molecules must brought be closer together in order to "connect" them to each other.
(While there is a "latent heat" equation to calculate the change in the bond internal energy during phase changes (when bonds are broken or made between individual atoms and molecules), we will focus primarily on changes in thermal internal energies, so only consider situations where there are changes in temperature, but no changes in phase.)
If there is no energy transferred into or out of the thermal internal energy of a system (as with the contents an extremely well-insulated Thermos® bottle), then it is effectively thermally isolated from the environment, and the heat exchanged between the system and the external environment is zero.
(Don't ever expect heat to spontaneously flow from a lower temperature object to a higher temperature object--unless you "do work" (expend mechanical energy) to make this happen, which is why it will cost you to run a refrigerator or air conditioner to remove heat from the low temperature contents, and dump it to the warmer environment outside. We'll focus on the "natural" direction of heat flow that occurs between two different temperature objects that thermally interact with each other.)
When you substitute the individual ∆Etherm terms on the right-hand side of the equation with the equivalent m·c·∆T expressions, then this results in the oh-so-familiar-but-maybe-not-quite-so-meaningless-anymore "Q = m·c·∆T" equation.
Note that in the idealized case that the system is thermally isolated from both external agents and the environment, then the left-hand size of this equation would be zero. Then the individual energy terms on the right-hand side of this equation can then trade and balance amongst themselves, instead of with the outside world.
So now let's see how this transfer/balance equation can be applied to idealized situations where heat gain/loss exchanges with the outside world are negligible compared to the exchanges within a system.
Assuming that the seafood and salt block system is thermally isolated from the environment (such that Qext = 0), which thermal internal energy experienced a greater amount of change: the seafood, or the block?
As the seafood cooks, its internal thermal energy increases, as the temperature of the food increases. (If you calculated the change in internal energy of the seafood, you would get a positive value, which is consistent with an increase.)
As the salt block cooks the seafood, its internal thermal energy decreases, as the temperature of the salt block decreases. (If you calculated the change in internal thermal energy of the salt block, you would get a negative value, which is consistent with a decrease.)
Since we are assuming idealized situations where heat gain/loss exchanges with the outside world are negligible compared to the exchanges within a system, then there is no heat given off or taken in from the environment, so the left-hand side of the transfer/balance equation is zero:
Qext = ∆Eseafood + ∆Esalt block,
0 = ∆Eseafood + ∆Esalt block,
then we are only left with the changes in the thermal energies of the seafood and the salt block:
0 = ∆Eseafood + ∆Esalt block,
0 = (+) + (–).
Now we can see that amount that the seafood's internal thermal energy increases (where ∆Eseafood is positive) is directly related to the amount that the salt block's internal thermal energy decreases (where ∆Esalt block is negative), in order to equal the zero on the left-hand side of the equation. So the salt block's internal thermal energy "feeds" (or is "transferred to") the seafood's internal energy during this process.
Assuming that the meat and water system is thermally isolated from the environment (such that Qext = 0), which thermal internal energy experienced a greater amount of change: the meat, or the seafood?
Assuming that the whiskey and beer system is thermally isolated from the environment (such that Qext = 0), which thermal internal energy experienced a greater amount of change: the whiskey, or the beer?
(If you haven't noticed the type of vocabulary used in this presentation, we are deliberately avoiding the confusion between "hot" (in terms of high temperature, high thermal internal energy objects) and "heat" (thermal energy transferred between objects).)