Before revision:  We show that the differences between the exact solution and the exponential cooling law are not significant, and even negligible, for small surfaces of the order 10cm^2 . However, for larger surface sizes, the radiative cooling component may become comparable to the convective cooling component. Our results thus suggest that, in the absence of accurate temperature measurements, an exponential cooling law is accurate enough for  small-sized SoC systems that require low processing overhead.
After revision:  We show that the differences between the exact solution and the exponential cooling law are not significant, and even negligible, for small surfaces of the order 10cm^2 . However, for larger surface sizes, the radiative cooling component may become comparable to the convective cooling one. In other words, radiation becomes non-negligible for systems with a cooling surface larger than about 1\,dm^2. Otherwise for surfaces below 1\,dm^2, we show that the differences between the exact solution and the exponential cooling law becomes negligible. In the absence of accurate temperature measurements, an exponential cooling law is accurate enough for small-sized SoC systems that require low processing overhead.