It's been pointed out that the temperature should have been stated as 385 F and not 385C. That makes a substantial difference. I'd STILL recommend the test that I suggest at the end as a guide to what to expect. 385F = 196C
The formula I gave suggests a 5% reduction in lifetime under those conditions over 8 minutes. That would almost certainly be so far outside the sensible range of use as to ber very very very approximate - but shows how extreme even 196C is compared to 105C.
Unless the board is otherwise a complete write off, don't even think about it.
Apart from the effect on the capacitor the process will cause major damage to other components - see below. Aluminium "wet" electrolytics have a electrolyte with a boiling point roughly the same as water has. While some capacitors are made to withstand temperature will above water boiling point, most aren't. There is an extremely good chance of inflicting major damage to the capacitors.
There is a lifetime calculation formula for capacitors which almost certainly does not apply here - but "for fun" it predicts that the lifetime of typical psu caps would be about
2000 hours x 1/2^((385-105)/10) = about 1/500th of a second :-)!!!.
They'll last a bit longer than that, but you get the idea, I'm sure.
BUT if you REALLY want to try, see the suggestion at the end.
Even if it is wholly dead there are other things you can do which have more chance of fixing it.
What you propose has a very good prospect of doing major permanent damage.
Any plastic component on the board will melt below that temperature.
Of all the plastics you are liable to encounter only two have continuous service temperatures above water boiling point (100C / 212 F) - those are PTFE and PEEK and you will have little or none of either on your board. (Just maybe some PTFE in a connector).
Table of plastic characteristics here
Resoldering all the solder joints that you can get to MAY have a better effect.
There is no guarantee that the page you cited tells a genuine story. I have seen pages which make the most outrageous and certainly untrue claims complete with step by step instructions on how you too can waste time and money following their example.
Simple experiment:
Take a board that you do not value at all. Ideally with enough connectors etc to be vaguely similar in content type to the one you are thinking of incinerating.
Try it in the oven at the temperature that they suggest for the time that they suggest.
Report back
Added:
See this directly related article
Robustness of Surface Mount Aluminum Electrolytic Capacitors When
Subjected to Lead Free Reflow
Atmospheric pressure, or the lack thereof, does affect electronic components. Components in low to near-zero pressure tend to outgas, and while ICs are relatively simple to condition for this, parts like electrolytic capacitors will fail. Hence, components specifically designated for zero-pressure are used instead.
Radiation affects ICs in two ways:
Firstly, semiconductor behavior changes significantly under increased ionizing radiation, such as exists outside the earth's protective atmosphere, and in the highly ionized belts of the stratosphere. Hence, radiation-hardened parts are manufactured specifically for such purposes, and are used in space electronics.
Secondly, under normal operation (on the ground) the thermal output of any IC gets removed from the package by a combination of radiation and by being carried away passively by moving air... In low pressure or vacuum, only radiation of heat works, not passive air-borne cooling, thus changing thermal dissipation calculations for any component.
Thus non-traditional cooling mechanisms and considerably greater distribution of conductive cooling paths are required.
Regarding gas-related precautions for space electronics: Manned space vehicles have sometimes used oxygen enriched environments. This leads to a necessary rethinking of such circuit design elements as PCB spark gaps, which could lead to catastrophe.
Also, non-design sparking, such as due to motor / coil field collapse, metal contacts of switches, or just a loose connection, need to be eliminated entirely - much more critical than for normal earth atmosphere. Silicone-filled contact casings, like the classic oil-filled switches, are worth considering. Similarly, space-safe epoxy potting of practically all exposed metal including PCB traces, is a way to go.
Further, there is the whole thermal operation range to be considered, especially for unmanned craft: From very hot (due to solar exposure without atmospheric protection), to very cold (due to no "atmospheric" heat when facing away from the sun).
This cyclic heating and cooling causes potential metal fatigue, junction stress and fracture such as at solder joints, and loose contacts due to uneven mechanical expansion and contraction between different materials.
Finally, not all semiconductor components are specified for extremely low temperatures. While heat might be an obvious concern, cold is an equally big issue. Some parts are specifically manufactured, and tested, for extreme low temperature operation. For other parts, the component behavior changes need to be taken into design consideration. For instance, the simplest PTC resettable fuse is no longer a trivial circuit element in space electronics.
I hope this has given an insight into just some of the factors around your question. For the rest, a search engine is your best bet.
Best Answer
The first thing to mention is that these grades are all manufactured identically, and their performance is measured so that they can be put into one of these three bins. There might only be two real bins, but at this point it's speculation.
The temperature plays a part in the speed as well - the higher the temperature, the lower the maximum clock frequency. At cold temperatures, the chip will run faster. Cold temperature failures are usually hard failures, in the sense that reducing clock frequency won't fix things. "Worst case" depends on your application. Here are a few scenarios that could happen.
There is a distinct possibility that they only qualified the industrial temperature range part because a wider specification means more time and money. In that case, all grades will probably work down to -40C. There may also be more durable packaging with the industrial range part.
If you are using this part for a hobby project, you may be comfortable "risking it". You may also be able to qualify individual parts, but any manufactured device will be a tough sell without the wide temperature range chips.