James Clerk Maxwell popularized this method of dimensional analysis; in fact, before him, dimensions were a mishmash, unstandardized, and such analysis was impossible.
I'll give you silicon, which has specific-heat about 3X higher than tungsten.
At 2 picoJoules/(cubic_micron*degree Centigrade), suppose we want to short the output driver of a microcontroller? That driver is 100 micron * 100micron (its a powerful transistor), with 0.1 amp short-circuit ability. Assume 2.5 volts.
How long before the transistor reaches 1,025 degrees Centigrade? starts at 25C.
Our power is I*V = 0.1amp * 2.5 volts = 0.25 watts, or 250Billion picoJoules/second. The volume of silicon? Assume we'll only heat the top 100microns of the Integrated Circuit during our experiment (that depth has a thermal TimeConstant of 114 microseconds, and in that time "most" of the heat remains in that 100micron thickness. Our total volume is 100*100*100U or 10^6 cubic microns.
What is our rate-of-change-of-temperature? we want degrees/second as dimensions for our answer.
The only bit of info we have with seconds is the power: 4 seconds/joule
We want to cancel the "joules" so multiply 4seconds/joule by specific-heat of silicon
$$4 seconds/joule * 2 picoJoule/(cubicmicron * degree Cent) $$
Our rate of temperature rise is $$8 picoseconds/(cubicmicron *degree Cent)$$
And we have 1Million cubicmicrons of silicon. We need to cancel 'cubicmicron' in our answer, so multiply the answer by 10^6 cubicmicron, and we get
$$8 Million picoseconds/degree Cent$$ or $$8microseconds/degree Centigrade$$
We wanted 1,000degree Cent increase in temperature, thus 8,000 microseconds or 8 milliSeconds is the answer.
We initially assumed ALL THE HEAT would remain inside 100*100*100 micron cube.
In 8 milliSeconds, heat will have moved outside the cube.
A different method is needed for a correct answer.
And thank Maxwell, also the investigator of viscosity, for this method.