That depends on how you define and measure "thermal energy". The
concept is not well-defined or broadly accepted in thermodynamics
because the "thermal energy" is typically assumed to refer to
internal energy present in a system due to its temperature.
Internal energy can be changed without changing the temperature,
and there is no way to distinguish which part of the internal
energy is "thermal". Instead, the appropriate thermodynamic concept
when talking about something "thermal" is HEAT: defined as a
transfer of energy due to differences in temperature (just
as work is another type of transfer of energy). Heat and work
therefore depend on the path of transfer and are not state
functions, whereas internal energy is a state function. If we
equate "thermal energy" with "internal energy" then we are talking
a "state function" which requires that we choose the state that we
will measure relative to. Altitude is a good example of a state
function. We can define altitude as either the distance between the
ground and an airborne item (like an airplane or balloon) or we can
define altitude as the distance between sea-level and the height of
the item. Depending on what we choose as "zero" we get different
values. Internal energy is also dependent on total mass, so it
would depend on the size of the iceberg and the size of the pool.
If you chose to use 0 K as your reference point and had a very
large iceberg and a very small pool, the internal energy (or
"thermal energy" if we equate the two terms) of the iceberg would
be greater. If you choose room temperature the iceberg will have a
NEGATIVE internal energy while any pool of boiling water would have
a POSITIVE internal energy (hence "more" energy). If you choose
something like ice at 0°F, then the size of the two comes into play
because both will be positive.
