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.
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.
See this directly related article
Robustness of Surface Mount Aluminum Electrolytic Capacitors When
Subjected to Lead Free Reflow
Thanks to 0x6d64 for pointing out the C/F discrepancy.
The data sheet says:
Rated for full −50° to +300°F range
In C that is -45°C to 148°C - not enough for your needs.
Your main problem at that kind of temperature is going to be the melting of the solder you're using to attach the LM34CZ.
Personally I'd use a thermocouple. Rated an hundreds of degrees (usually 400+), they allow you to keep all sensitive circuitry away from the hot area.
You'll need a converter chip to allow you to reliably use a thermocouple of course. Most people use the MAX6675, but that is being phased out to be replaced by the MAX31855.
Both are surface mount, so you'll need to etch a PCB to mount it on, or get a breakout board (8 pin SOIC).
Both the chips are pin compatible with each other, and provide an SPI interface the Arduino can talk to easily.
I have had a MAX6675 working on my Arduino, and am waiting for some MAX31855's to arrive so I can check to see if my Thermocouple Library for the Arduino works with them.
All semi-conductor characteristics are affected by Boltzman statistics relating charge carrier densities with respect to temperature. The hotter it is the more intrinsic carriers are present, at some point the intrinsic carrier concentration gets so high that any doping (n-type vs. p-type) gets wiped out. That is at high temperatures.
A conductor has the characteristic that as you heat it, the carriers are more mobile and collide more and resistance goes up. A Semi-conductor has the characteristic that as you heat it up, more carriers are present and the resistance goes down.
So it's natural to see that there are limits. Why particularly those temperatures, I don't know, I'm sure some one will come up with the historical answer. However, it's very celar that some temperature must be selected, because if you design for a very broad temperature range then some other performance metric will be compromised, like speed or margins.
Designs are specified over what are called PVT corners, as in Process, Temperature and Voltage corner cases.