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I don't think you have to restrict the work term to zero to talk
about increasing the thermal energy.
In terms of your example of the
baby bottle, with some water in it, standing at rest on a table, if
you tilt the nipple over by pushing the tip of it to one side without
changing the orientation of the rigid part of the baby bottle you
increase the elastic energy of the system,
if you pick the bottle up
and shake it rigorously for for a few moments and then set it back
down you have increased the thermal energy of the system, and if you
throw it across the room, starting from when you picked it up and
ending before it hits anything, you have increased the kinetic energy
associated with the motion of the center of mass of the object.
Based on your equating it to "caloric" I think you have chosen a
definition of thermal energy that is easy to criticize.