  A new global analytical model of the heat dissipation process that occurs in
passively-cooled embedded systems is introduced, and we explicit under what
circumstances the traditional assumption that exponential cooling laws apply in
such context is valid. Since the power consumption and reliability of
microprocessors are highly dependent on temperature, management units need
accurate thermal models. Exponential cooling models are justified for
actively-cooled systems. Here, we analyze the tractability of the cooling law
for a passively cooled body, subject to radiative and convective cooling,
including internal heat generation. Focusing then on embedded system-like
objects, we compare the performance difference between our new passive cooling
law and the conventionally-used exponential one. We show that, for quasi
isothermal cooling surfaces of the order of 1\,dm$^2$ or greater, the radiative
cooling effect 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 model is shown to be accurate enough for systems, such as
small-sized SoCs, that require low processing overhead.
