It's all about thermal mass.
Ultimately, this question is talking about how long it takes for life to die outside the 'ideal' conditions in which it thrives. As has been described in other answers, there are a wide range of conditions that impact this. Ultimately though, thermal mass is what makes all the difference.
So what is thermal mass?
For the purposes of this answer, we can describe it as any mass which has the ability to absorb and retain heat when its cooler than the environment, leeching it out over an extended period when the mass is warmer than its surroundings.
On Earth, we have the oceans and our atmosphere. The atmosphere retains a lot of heat (thanks to greenhouse gases) and traps it close to the surface. Thing is, the atmosphere is not a particularly good thermal mass. That's why temperature differentials between night and day exist.
That said, water does a much better job. If you live on a coastline, you'll know that the difference between night and day temperatures aren't as large as the difference between night and day further inland, particularly in deserts. Why? Well, the water on the coast retains a lot of the heat through the day and the atmosphere gets the benefit of that on a form of delayed release.
SCUBA Divers will tell you that temperatures in May (Southern Hemisphere) are still quite warm because the summer heat hasn't completely left the water yet.
So; if you have a large amount of water on your planet, you'll fare better than if you don't. Some measure of greenhouse gasses are necessary, but will cause problems when you're too close to the sun. As as been said in other answers, it's the too close part that you'll have the biggest problems with, especially if you have greenhouse gasses in the atmosphere to retain heat. The ocean will help absorb some of that heat, but you'll still want shelter from it during that part of the orbit.
You'd also want a high O2 atmosphere if possible Why? Because you want the extreme sun to produce large amounts of Ozone (O3) during the hot periods to assist with blocking cosmic radiation. Ozone is particularly useful here as a support to the magnetic field of the planet as it's temperature based and is naturally produced when it's needed most; on hot days (in this case closer to the sun)
It's not all good news though. Thermal mass can even out the extremes, but you still need quite diverse life capable of a very wide temperature variation.
Woolly Mammoths (as an example) would overheat in our current climate. Many animals on Earth are adapted to either warm climates or cold climates. Variation (lunar cycles, day/night, seasons, etc.) does drive a lot of the processes that allows life to grow and thrive, but the variations can't be too large otherwise the animal or plant needs concurrent yet contradictory adaptations to survive. Cactii don't do well in tropical climates, for instance. They REALLY don't do well in the arctic. Polar Bears would struggle in Mexico; you get the general idea.
It's possible that your life would find ways around this, and certainly aquatic life is far more possible in this scenario, but that leads to another consideration; ocean currents.
Most ocean life on Earth exists because of underwater currents that have been stabilised for some time. These bring plankton and other creatures through set zones, where larger animals feed on them, where even larger animals feed on them, etc. This creates reliable feeding patterns around the world's oceans, meaning that life specialises in exploiting that pattern and diversity is assured. With the massive temperature variations you're describing, it's possible that those feeding patterns wouldn't occur and the weather would be more chaotic.
One of the reasons that Neptune (for example) seems to have winds ripping over its surface at incredible speed and with no apparent Coriolis effects is that it's so far away from the sun. Very little energy is being introduced into its planetary system, so when the wind starts, there's very little to stop it.
Your planet on the other hand is constantly getting (intermittent) dumps of large amounts of energy into its atmospheric and water stores. That's likely to create all sorts of chaos in the weather, currents etc.
This doesn't make life impossible, but it does make it hard. Food becomes less predictable. Birth rates become lower as a result.
Is life on such a planet possible? Sure, given the right thermal mass considerations. Is life so possible that it's likely intelligent life might evolve? No, I'm afraid not.
We really don't spend a lot of time thinking about it, but we're incredibly lucky to have this planet. It's like winning the lottery hundreds of thousands of times in a row. Even then, conditions are not always (and certainly haven't always been) ideal. On this world you're describing, the chances of intelligent life evolving are reduced by virtue of the fact that life won't thrive quite the way it does on Earth. It might be a reasonable colonisation site, but we not about to meet our equals there I suspect.