In superstring theories, there exist various dilaton and modulus fields who
se masses are expected to be of the order of the gravitino mass m(3/2). The
se fields lead to serious; cosmological difficulties, the so called "cosmol
ogical moduli problem,'' because a large number of moduli particles are pro
duced as the coherent oscillations after primordial inflation. We make a co
mprehensive study of whether the thermal inflation can solve the cosmologic
al moduli problem in the whole modulus mass region m(phi) similar to 10 eV-
10(4) GeV predicted by both hidden sector supersymmetry (SUSY) breaking and
gauge-mediated SUSY breaking models. In particular, we take into account t
he primordial inflation model whose reheating temperature is so low that it
s reheating process finishes after the thermal inflation ends. We find that
the above mass region m(phi)(similar or equal to m(3/2)) similar to 10 eV-
104 GeV survives from various cosmological constraints in the presence of t
hermal inflation. [S0556-2821(99)01220-5].