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er, unless you installed the coretemp plug-in and I do not think you have because on my machine Riva says "CPU0 temp... CPU1 temp... , the "Core temp" in Riva Tuner is your GPU core temp. You are comparing apples and oranges (cpu vs gpu).
Now slap yourself on the forehead and say "doh!"
As far as the difference in everest it might be normal, might not, open task manager and see what is running on each core or run Orthos or some other utility that loads the cores so that you can assume about the same load on each core with that load being much larger than anything else running on the machine and then look at the difference, a few deg C is pretty common, but yours is fairly high. It could just be software running but if not, /shrug look at your heatsink mounting is about all you can do about it.
say stick with RivaTuner