The large area ($ \rm 560 \, m^2$) GRAPES-3 tracking muon telescope located at Ooty, India has been operating uninterruptedly since 2001. Everyday it records $ \rm 4\times 10^9$ muons of energy $\rm > 1 \, GeV$ with an angular resolution of $\rm \sim 4^{\circ}$. Atmospheric temperature variation affects the rate of decay of these GeV muons produced by the galactic cosmic rays (GCRs), which in turn modulates the intensity of detected muons. Since the daily temperature induced variation combines with the diurnal modulation of the GCRs by the magnetized solar wind, it becomes rather difficult to segregate the respective contributions of these two phenomena. A small seasonal variation in the intensity of cosmic ray muon ($ \rm \sim 0.4\%$) with periodicity $\rm \sim $ 1 year (Yr) was measured by analysing the GRAPES-3 data of six years (2005-2010). The effective temperature `$\rm T_{eff}$' of the upper atmosphere above Ooty also displayed a similar periodic variation with an amplitude of $\rm \sim 1 K$, which was responsible for the observed seasonal variation in the muon intensity. At GeV energies, the muons detected by the GRAPES-3 show an anti-correlation with $\rm T_{eff}$ calculated by using a hadronic attenuation length $\lambda$. Using the fast Fourier transform (FFT) technique and making use of the anti-correlation between the seasonal variation of $\rm T_{eff}$ with the muon intensity, we calculated the temperature coefficient $\rm \alpha_T$. The magnitude of $\rm \alpha_T$ was found to scale with the assumed attenuation length $\rm \lambda$, which we varied within a range of 80-180 $\rm g cm^{-2}$. However, the actual magnitude of the correction was found to be independent of the value of $\rm \lambda$.