  We study thermal correlation functions of the one-dimensional impenetrable
lattice anyons. These correlation functions can be presented as a difference of
two Fredholm determinants. To describe large time and long distance behavior of
these objects we use effective form factor approach. The asymptotic behavior is
different in the space-like and time-like regions. In particular, in the
time-like region we observe the additional power factor on top of the
exponential decay. We argue that this result is universal as it is related to
the discontinuous behavior of the phase shift function of the effective
fermions. At particular values of the anyonic parameter we recover asymptotics
of spin-spin correlation functions in XXO quantum chain.
