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I'm not quite sure what you are referring to as high temperature but some years ago I designed power supplies for going down oil wells where they reach ambient temperatures of around 200C.
This is a huge subject but here are a few guide lines:
1] Conventional PCB materials will soften or burn at these temperatures, both are bad news in environments that combine high vibration and high temperature; you will need to use special PCB laminate that is intended for creating 'burn in' fixtures.
2] You will need high melting point solders that do not soften at high temperature or else with the added disipation of the power components you will find components coming off.
3] If you have any magnetic components in your design then you need to consider carefully the Curie point of the magnetic materials as above the Curie point temperature the material will suddenly lose its magnetic properties.
4] The best capacitor dielectrics that you can use are ceramic (COG), glass (Corning make glass caps) and PTFE, wet tantalum used to be usable at very high temperatures but are no longer made as far as I know.
5] Semiconductors are a whole subject in their own right but here goes:
Silicon is approaching intrinsic conduction at these temperatures but can be used in a very derated design with some thought; dielectrically isolated switches or switches made using CMOS on Sapphire (Peregrine Semiconductors) can be used, I think Intersil (used to be Harris) still do op-amps that are specified at these temperatures.
When biasing a transistor you must realise that the collector base leakage may exceed the base bias current if you are not careful so you need to consider this carefully and add a matching leaky junction to sink the leakage current.
With FETs the gate current will double approximately every 10C so you will need to consider that in any circuit that you design too.
GaAs rf components will often work happily at these temperatures as will SiC and GaN.
Very few components will actually specify operation at these temperatures so you will need to use the guidelines above, read up on the many failure mechanisms, do lots of qualification and experimentation and calculate such things as MTBF from Arhenius plots.
One last thing, if you're going to work up at 300C and beyond then consider using tubes rather than semiconductors - you can turn the heaters off at these temperatures and they carry on working!