From the definition:
dQ/dt=-(T-Tout)A/RSI
From the first law of thermodynamics and ideal gas theory:
Q=U=(5/2)nRT
dQ=(5/2)nRdT
(5/2)nR(dT/dt)=-(T-Tout)A/RSI
dT/(T-Tout)=-(A/RSI)/[(5/2)nR]dt≡-βdt
Integrate from t=0 to t and from T=T1in to T:
ln[(T-Tout)/(T1in-Tout)]=-βt
(T-Tout)/(T1in-Tout)=e-βt
T=Tout+(T1in-Tout)e-βt=67+73e-βt