Does the entropy of the gas increases with increasing temperature

Entropy increases with increasing temperature. But I am confused with the equation, entropy S=dq/T, which shows that temperature is inversely proportional to entropy. Can anyone explain to me? Thanks :/

We can use Tds equation for gas phases in internal reversible process.
Tds = dh - vdp
ds = dh/T - (v/T)dp, to simplify, let the process isobaric, p = constant
ds = dh/T, dh = Cp*dT
ds = (Cp/T)dT
s2-s1 = Cp* ln(T2/T1)
If T2 > T1, then s2 > s1
Which means as temperature increases then entropy also increasing.

The equation S=dq/T(Clausius inequality) indicates entropy change from heat transfer, not solely by temperature change.