  In this paper, we initiate the study of finite temperature quantum field
theories (QFT's) on the Moyal plane. Such theories violate causality which
influences the properties of these theories. In particular, causality
influences the fluctuation-dissipation theorem: as we show, a disturbance in a
space-time region $M_1$ creates a response in a space-time region $M_2$
space-like with respect to $M_1$ ($M_1\times M_2$). The relativistic Kubo
formula with and without noncommutativity is discussed in detail, and the
modified properties of relaxation time and the dependence of mean square
fluctuations on time are derived. In particular, the Sinha-Sorkin result
\cite{sorkin-sinha} on the logarithmic time dependence of the mean square
fluctuations is discussed in our context.
  We derive an exact formula for the noncommutative susceptibility in terms of
the susceptibility for the corresponding commutative case. It shows that
noncommutative corrections in the four-momentum space have remarkable
periodicity properties as a function of the four-momentum $k$. They have
direction dependence as well and vanish for certain directions of the spatial
momentum. These are striking observable signals for noncommutativity. The
Lehmann representation is also generalized to any value of the noncommutativity
parameter $\theta^{\mu\nu}$ and finite temperatures.
