  The processes controlling the complex clump structure, phase distribution,
and magnetic field geometry that develops across a broad range of scales in the
turbulent interstellar medium remains unclear. Using unprecedentedly high
resolution three-dimensional magnetohydrodynamic simulations of thermally
unstable turbulent systems, we show that large current sheets unstable to
plasmoid-mediated reconnection form regularly throughout the volume. The
plasmoids form in three distinct environments: (i) within cold clumps, (ii) at
the asymmetric interface of the cold and warm phases, and (iii) within the
warm, volume-filling phase. We then show that the complex magneto-thermal phase
structure is characterized by a predominantly highly magnetized cold phase, but
that regions of high magnetic curvature, which are the sites of reconnection,
span a broad range in temperature. Furthermore, we show that thermal
instabilities change the scale dependent anisotropy of the turbulent magnetic
field, reducing the increase in eddy elongation at smaller scales. Finally, we
show that most of the mass is contained in one contiguous cold structure
surrounded by smaller clumps that follow a scale free mass distribution. These
clumps tend to be highly elongated and exhibit a size versus internal velocity
relation consistent with supersonic turbulence, and a relative clump
distance-velocity scaling consistent with subsonic motion. We discuss the
striking similarity of cold plasmoids to observed tiny scale atomic and ionized
structures and HI fibers, and consider how the prevalence of plasmoids will
modify the motion of charged particles thereby impacting cosmic ray transport
and thermal conduction in the ISM and other similar systems.
