  We studied the temperature effect in isospin-singlet pairings in Gamow-Teller
excitations. We use theories of a hole-particle in the mean field shell model
studied decay transition using the one-particle-one-hole model for the
$\beta$-decay of odd-even isotopes and the two-particle-hole models for the
$\beta$-decay of even-even and/or odd-odd isotopes. Our reference isotopes for
the one-particle-one-hole model are \ce{^{15}O}, \ce{^{15}N}, \ce{^{17}F}, and
\ce{^{41}Sc}, whereas for the two-particle-hole model we use \ce{^{16}N} (for
$\beta^-$-decay) and \ce{^{56}Ni} and \ce{^{40}Sc} (for $\beta^+$/EC).
  The calculations involve evaluating the matrix elements of Gamow -Teller and
Fermi transitions, then calculate the reduced transition probabilities of
Gamow-Teller and Fermi, from which we evaluate the half-lives and the strength
function $ft$. The results are compared with the available experimental data.
For one-particle-one-hole model we found there is a deviation from experimental
values which indicates that the model is not valid for beta decay for the
even-even nuclei in the ground state due to the residual nucleon-nucleon
interaction. As for a two-particle-hole model, we calculated the transition
amplitude, from which we calculated the strength of the transition $\log ft$
values. We found an excellent agreement between experimental and theoretical
results.
  By drawing the relationship between temperature versus $\log ft$ values, we
found the general trend is that the strength function values slowly decrease as
temperatures increases. There are fluctuations $\log ft$ due to the strongly
dependent of $\log ft$ on the shell configuration of the valence nucleons.
