How quickly does a supernova heat up/expand? Suppose there's a star out there that's a lot more massive than the Sun.

Suppose further that orbiting this star is a planet not unlike Earth. Water, oxygen, civilization, and all.

Now the star decides to go supernova. How quick, or slow, is the process?

How long will it take it to heat up to make life on that planet impossible? A month? A year? A hundred years? A thousand years?

And how long will it take for the supernova to engulf the planet? A day? A month? A year? A million years?
Ricky, it is very rapid. The core collapse and initial neutrino burst takes seconds to tens of seconds. We don't normally think about neutrino interactions, but so many are released that even this might be a problem for a nearby habitable planet. It then takes a few hours for the shockwave from the core collapse and bounce to make it out to the surface, accompanied by an intense flash of UV light that would likely sterilise anything in its planetary system. The outer layers of the exploding star are hurled out at around 1000 km/s, so could travel an astronomical unit in a day or so.

The supernova continues to become more luminous for about a week thereafter, increasing in luminosity, from what must have already been enormous (thousands of solar luminosities) by another factor of $10^5$. The equilibrium temperature of any planet scales roughly as $L^{1/4}$, so temperatures would rise by more than an order of magnitude in a week.