We study a series of N = 1 supersymmetric integrable particle theories
in d = 1 + 1 dimensions. These theories are represented as integrable
perturbations of specific N = 1 superconformal field theories. Starti
ng from the conjectured S-matrices for these theories, we develop the
Thermodynamic Bethe Ansatz (TBA), where we use that the 2-particle S-m
atrices satisfy a free fermion condition. Our analysis proves a conjec
ture by E. Melzer, who proposed that these N = 1 supersymmetric TBA sy
stems are ''folded'' versions of N = 2 supersymmetric TBA systems that
were first studied by P. Fendley and K. Intriligator.