Electronics in high temperature - operating 30 mins - 2 hours, up to 500 °F - possible?
This is well beyond the ratings of most parts. You can expect outright failures, major departures from guaranteed specs, flaky (eg. partial) operation, huge leakage and so on. Unless you buy qualified parts, you are on your own, so you are looking at major costs, and it may not be possible to thoroughly test some parts without inside information. 

Downhole instrumentation can at very high temperatures, but parts that are qualified for that operation are very expensive (eg. Honeywell) and have rather disappointing performance to boot. 

It's possible to design an electronics package that will survive an external temperature of 260°C for a substantial period of time, by keeping the internal temperature to something reasonable like &lt;125°C, but that's more of a mechanical engineering problem than an electronic one. For example, by use of good insulation and a phase-change material.