  We investigate thoroughly the temporal evolution of the universe temperature
as a function of the Hubble parameter associated with the Stochastic
Gravitational Wave (SGW), that formed at the cosmological QCD phase transition
epoch to the current epoch, within the Generalized Uncertainty Principle (GUP)
framework. Here we use GUP version which provide constraints on the minimum
measurable length and the maximum observable momentum, that characterized by a
free parameter $\alpha$. We study the effect of this parameter on the SGW
background. We show that the effect can slightly enhance the SGW frequency in
the lower frequency regime which might be important in the detection of SGW in
the future GW detection facilities.
