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58 and 97 follows the route the railroad takes over the Cascades, it's pretty flat. None of the constant ups and downs like on I-5 in southern Oregon. You also miss the Siskiyou grade. I'd take 39 and 139 from Klamath Falls to Susanville, CA then 395 to Reno. 80 and 50 east to Fallon, then 95 south to Las Vegas.
Nevada will be hot, no way around it. But so will be CA's Central Valley. Expect temperatures in the 90s to low 100s either way.
I-5 south of Eugene is constant ups and downs until Grants Pass, then you have the Siskiyou Grade between Ashland and Redding. And another 6000 ft. climb on I-80 between Sacramento and Reno.
IMO trying to get to Reno in a single day is pushing too hard. Especially in hot weather with an older RV. Google Maps figures driving time by dividing the distance along each stretch by the speed limit, you won't be doing this in an older RV. It doesn't include time spent getting gas, getting meals and taking rest stops, etc.
It's 769 miles from Corvallis to Reno. Figure on an average speed in an RV (including fuel and rest stops) to be about 50 MPH and you're looking at 16 hours of driving.