As others have said /hinted at - LiIon highly unlikely to work unless you get specially made Lithium cells (usually primary/non-rechargable) - they do exist, but very specialised. Look at what companies like Steatite, Creasefield, ElectroChem etc.. recommend for high-temp down bore applications.
Alot of the silicon will work at 170C, although you'll have to try it on a case by case basis (testing will be the only way to proceed). Most modern IC packaging will also work, for a limited period at least, high temperature lead-free solder, and probably find somesort of silicone potting compound to hold everything in place.
Tg170 or higher PCB substrate, forget the cheap PCB services.
Old school RAM will probably work, FLASH probably won't. Build in error detection/correction when storing your data. Also old school processors with as little going on as possible - run them slow. RTC - be really simple and record samples at known intervals, don't overcomplicate design. What is the bandwidth of what you are recording? Temperature/pressure?
Understand the failure mechanisms of your design, avoid thermal shock/uneven heating and look up electromigration in silicon due to thermal effects. Automotive passives (capactiors) will be less prone to cracking due to the flexiable design of the terminations. Even solder flux contaminants could kill your design. Design for low power, use big junctions - cause any extra heat might tip you over the edge.
Good luck & TEST.