Did the components really heat up this quickly?
I thought about this some, and I ended up doing some thermodynamics. This will be rather mathematical and very likely quite unhelpful, but here it is.
Let's say your CPU has a thermal mass C (Joules/Kelvin) and outputs a constant power P (watts). It is connected to the outside air by the heatsink, which has a thermal conductance S (watts per kelvin). The total amount of heat in the CPU is H = TC where T is the temperature of the CPU relative to ambient.
Then the total heat change of the CPU is: dH/dt = P - ST
We can re-express this: C(dT/dt) = P - ST
then we can separate variables and integrate to get the result
T = P/S + (Ti - P/S) * exp(-S/C * t)
where Ti is the temperature at some arbitrary time 0. From this, we see that after infinite time, we expect the CPU temperature to be P/S, as we would expect from simple thermal equilibrium.
If we knew (or guessed) P, S, and C, we could easily determine the answer to the question "Did the components really heat up this quickly?" Or, somebody else with a better sense for these things might have an intuitive answer.
Anyway, what I do know is that during startup and while in BIOS, the CPU runs at full-tilt, 100% power. So it is quite possible that the CPU did heat up 5 degrees in 15 seconds - especially because at such close temperatures to ambient, the heatsink will do almost nothing.