That's a good question. I don't really know the answer.
I guess the closest I can say is that, user 3v0 asked about an object getting hotter as it's lifted up against gravity and I don't know the answer.
If you have three bricks, one on each level of shelving, the uppermost one has the most potential energy. If the three bricks, themselves, are examined, is that energy difference apparent in any measurable way? Does the energy only manifest itself by the way it acts when it moves (in other words, is it the environment that interacts with the brick as it falls or is lowered that makes the brick seem to have had more potential energy?
Unfortunately, perhaps, there's no shortage of nit picking that can be done with something like this. Can the heat in the brick convert some water to steam and if the steam does some work, is that the same as connecting the brick to the pulley? But, even there, does the upper shelf brick have the capacity to make the water hotter? Directly from its inherent heat or only if you sum it's heat and kinetic motion as it's lowered?
I'm not trying to nit pick, I'm trying to get you to be VERY precise and unambiguous about what you mean. If you want to talk about heat energy fine, and certainly there is some potentional energy to warm water (assuming that the water isn't in the same room at room temperature).
However, IF we're going to have this conversation then we need to be very precise and unambigous about how we define the different types of energy and what exactly those definitions mean, otherwise this conversation will be frustrating and a big waste of time as nothing will be accomplished.
Most of this thread is wrought with vaguety, everyone assumes that everyone knows what they mean when they say "energy" or "knetic energy" or "heat energy" or "work" or "pressure" etc. When in MOST cases those words mean different things to different people.
So BEFORE we continue this conversation we should first define energy, potentional energy, heat energy, kinetic energy etc. This might sound like a waste of time, but I assure you it will save pointless arguing about definitions of words later.