  We study the large distance expansion of correlation functions in the free
massive Majorana theory at finite temperature, alias the Ising field theory at
zero magnetic field on a cylinder. We develop a method that mimics the spectral
decomposition, or form factor expansion, of zero-temperature correlation
functions, introducing the concept of "finite-temperature form factors". Our
techniques are different from those of previous attempts in this subject. We
show that an appropriate analytical continuation of finite-temperature form
factors gives form factors in the quantization scheme on the circle. We show
that finite-temperature form factor expansions are able to reproduce expansions
in form factors on the circle. We calculate finite-temperature form factors of
non-interacting fields (fields that are local with respect to the fundamental
fermion field). We observe that they are given by a mixing of their
zero-temperature form factors and of those of other fields of lower scaling
dimension. We then calculate finite-temperature form factors of order and
disorder fields. For this purpose, we derive the Riemann-Hilbert problem that
completely specifies the set of finite-temperature form factors of general
twist fields (order and disorder fields and their descendants). This
Riemann-Hilbert problem is different from the zero-temperature one, and so are
its solutions. Our results agree with the known form factors on the circle of
order and disorder fields.
