I may be answering something you weren't asking, but the spikes sound pretty normal to me, meaning I've observed that spike on multiple engines that seemed otherwise fine.
My belief is the spikes are due to LATENT heat buildup in the engine during the hard run. While running hard, a lot more heat is produced and the internal temps are higher than at idle, but there's a lot more cooling water going through the system, such that the RATE of wicking away BTUs is much faster than it is down at idle. The temp sensor only sees temp at one spot though, so we have a tendency to think about only that one. That measured temp might be close to the same at warmed-up idle ands during the hard run, even though the cylinder walls would be much hotter during the hard run.
The upshot is that when you back down from the hard run, your cooling flow drops way down. But there's still a lot of heat built up further in the engine that is making its way out to the "edges" so to speak. Because the relative trickle of cooling flow can't haul heat away as fast, the temp where the sensor sits rises for about a minute or two, until the smaller cooling flow takes care of the backlog.
That addresses the spike part (if that was even part of what you were asking ), but not the difference in absolute temp at steady state. That sounds like it COULD be related strictly to raw water temp, depending on our system, but I'd have my eye closely on it, recording measurements at different spots, in case something else was involved, restricting flow. I'd bet it's more than just the lake temp. The ten degree difference seems like a lot to me. How much warmer is the lake than normal?
"I don't have time to get into it, but he went through a lot." -Pulp Fiction