From the definition:

dQ/dt=-(T-T^out)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-T^out)A/RSI

dT/(T-T^out)=-(A/RSI)/[(5/2)nR]dt≡-βdt

Integrate from t=0 to t and from T=T₁ⁱⁿ to T:

ln[(T-T^out)/(T₁ⁱⁿ-T^out)]=-βt

(T-T^out)/(T₁ⁱⁿ-T^out)=e^-βt

T=T^out+(T₁ⁱⁿ-T^out)e^-βt=67+73e^-βt