  Firstly, nonlocal field theories will be motivated, primarily in the gravity
sector. We discuss how nonlocal theories of gravity can circumvent typical
problems of finitely-many higher derivative theories and can, among other
things, be either ghostfree and (potentially) renormalizable and yield a
non-singular Newtonian potential. Afterwards we motivate finite temperature
field theory, also known as thermal field theory, and study the thermodynamic
behavior of both a local and a nonlocal scalar field theory. We compute
(primarily leading-order) thermal corrections to the partition function for in
low- and high- temperature expansions and calculate the thermal mass which is
acquired through continuous interactions with the heat bath. We prove that the
nonlocality does not contribute to the partition function of the free nonlocal
theory. The presence of the nonlocality can only be noticed through
interactions and we conclude that the partition function of the local and the
nonlocal scalar theory are fundamentally different when interactions are
included. We explain from both a mathematical and physical point of view why
the nonlocality can only be noticed at the level of interactions and conclude
that this cannot be generalized to arbitrary nonlocal modifications -- only
those which do not introduce new poles in the propagator. We study whether our
results can be reconciled with the stringy thermal duality and the conjectured
Hagedorn phase and conclude that the former is violated, while Hagedorn
behavior emerges in the high temperature expansion of the nonlocal scalar
theory. We will interpret all these results.
