If I exercise by weightlifting, I can "burn calories". The way I
understand the process is as follows: when I'm moving the weight up,
the energy from chemical bonds turns into potential energy of the
weight. When I'm moving it down, though, the same potential energy
turns into heat inside my muscles and ligaments. The heat is then
dissipated around - that's why I'm sweating.
I think a biological perspective might help here. When you activate your muscles, they use a molecule called ATP as "fuel". When the ATP is used, it releases chemical energy. Some of that energy is used in the actual muscle contraction, but the process isn't 100% efficient, so a lot of that energy is wasted as heat.
It's like burning gasoline in a car. Some of it is used in the actual function of the car, but if I recall correctly, gasoline engines are only something like 20-30% efficient; the rest is wasted as heat.
On top of that, there is only a very small amount ATP stored in our cells, so our bodies have several mechanisms for producing it as needed (e.g., converting glucose to ATP). These processes are also not 100% efficient and will produce heat as a by-product (along with other things like the lactic acid that makes our muscles sore).
That's where the heat in your muscles is coming from. There technically is also friction as your muscle fibers contract and your body moves, but I'm not sure it generates a significant amount of heat relative to the chemical reactions.
Now assume that I'm unloading a truck, i.e., only moving weights down.
I'm now just using the potential energy to heat my body.
A physicist might have to correct my physics interpretation here: I think it's correct to say that when we lift an object, we are converting the chemical energy in our bodies to gravitational potential energy in the object.
When we lift an object, we use chemical energy to activate our muscles. When we lower an object, we are still using chemical energy to activate our muscles, but instead of doing it to lift, we are doing it to slow the rate of descent of the object. The heat our body generates comes from the inefficiencies of that process.
If my interpretation of this answer is correct, then it's correct to say that the loss of gravitational potential energy is being converted to chemical energy (Again, I'll let a physicist correct anything here). This is a little unintuitive to me as non-physicist because I think the statement is describing what is happening from a physics/mathematical perspective rather than what is happening from a biology and chemistry perspective.