  Phase-space Lagrangian dynamics in ideal fluids (i.e, continua) is usually
related to the so-called {\it ideal tracer particles}. The latter, which can in
principle be permitted to have arbitrary initial velocities, are understood as
particles of infinitesimal size which do not produce significant perturbations
of the fluid and do not interact among themselves. An unsolved theoretical
problem is the correct definition of their dynamics in ideal fluids. The issue
is relevant in order to exhibit the connection between fluid dynamics and the
classical dynamical system, underlying a prescribed fluid system, which
uniquely generates its time-evolution. \
  The goal of this paper is to show that the tracer-particle dynamics can be
{\it exactly} established for an arbitrary incompressible fluid uniquely based
on the construction of an inverse kinetic theory (IKT) (Tessarotto \textit{et
al.}, 2000-2008). As an example, the case of an incompressible Newtonian
thermofluid is here considered.
