Kinetic energy and collisions in cosmology? Objects in space time can move due to the expansion of spacetime itself (where objects that are sufficiently far apart would recede from each other due to the Hubble flow) and peculiar motions (which are deviations from the Hubble flow).
Having said this, are there any observed situations or cases where a celestial body/structure with a given amount of kinetic energy coming from both its peculiar motion and the movement due to the Hubble flow transforms that total kinetic energy into something else (like heat, when colliding with another object or structure)?
 A: First, ignoring issues with general relativity and cosmology, in classical physics the bulk center of mass energy of a system is conserved separately from the internal energy. This is why in thermodynamics we often simply work with a system in its rest frame.
Second, in general relativity, energy is not conserved, in general. Any attempt to talk about energy will be observer and coordinate dependent, and therefore not truly physical.
Third, there is a sense in which energy is locally conserved in general relativity. The easiest coordinate system to see this in are the locally inertial coordinates. To understand the dynamics of a faraway galaxy merger, arguably the most physically transparent approach is to remove the Hubble flow by working in locally inertial coordinates. So long as the merger takes place on time scales short compared to the expansion rate of the Universe, this frame is sufficient to capture "internal" dynamics of the system. You can then "boost" this frame to include the Hubble flow to see how the Hubble flow affects what we observe of the process; but on some level the expansion of the Universe was not really relevant to the process since by a nice choice of coordinates we could work out what was happening ignoring the Universe's expansion to a good approximation.
If this chain of logic doesn't satisfy you, then the kind of process you would need to find are processes with a natural length scale (time scale) of order the Hubble radius (inverse Hubble rate), so (today) of order 10 billion light years (10 billion years). The right way to understand this isn't in terms of the Hubble flow changing the energy flow, per se -- rather, I would say that for such processes, the expansion of the Universe cannot be ignored in any coordinate system. For such processes, the Hubble flow could have a non-negligible impact on the way the process proceeds. I am not sure if there are astrophysical processes in today's Universe occurring on such large scales, but there are processes in the early Universe where these effects did matter. For example, the duration of primordial nucleosynthesis, and therefore the distribution of primordial elements, depends on how the rate of fusion of light elements compares with the expansion rate of the Universe when the Universe is cool enough for protons and neutrons for form from the quark-gluon plasma and hot enough for nucleosynthesis to happen.
