I highly doubt your CPU is the issue causing heat. In sleep mode your CPU is not processing anything. I think the main cause is how the OS and the BIOS is being used in that power state and somehow causing the CPU fan to spin up. It is a good idea at least every four years or so to replace the thermal paste. To run Speedfan your not in the same sleep mode environment and in a booted environment so your variable for testing has changed. Even if you do find that your CPU is going beyond its thermal limit, it may not indicate that it's the source of the high RPM of the CPU fan while in a low power mode.
I'd just fully shut down the computer at all times. That right there will elevate the issue altogether. If you run something like Prime95 and watch your temps with Speedfan or CPUz and your temps are hitting over 55c, then either you need a better cooling solution both in the case and on your CPU or you need to reapply the thermal paste. In my PC using CPUz and running FSX which is a CPU orientated game, my temps don't go above 45C. Although, my case has 5 fans and the CPU fan is a Cooler Master Evo 212 which works quite well. I could even do a push, pull configuration but I don't really need to.
If you reapply the thermal paste, clean the majority off and use alcohol for the rest. Apply the alcohol to a paper towel. Get it as clean as possible. Add a drop of thermal paste to the center of the CPU and use a razor blade or a cut index card and spread the thermal paste over the CPU so the entire surface is covered. DO NOT overdo the thermal paste application. You just want a thin layer between your CPU and the heat sink. Other people seem to think just adding a drop of thermal paste in the center of the CPU is all you need to do. But I can tell you that I've pulled CPU heat sinks off and the CPU thermal paste was round and not fully covered.
You should use a static strap, but if you don't have that you can either touch the chaises of the case all the time, or keep the computer plugged in so that you have ground. Providing your wall outlet is in fact grounded. When I built my PC I never used a static strap because the damn thing broke and my wall outlet is not grounded. So I'd keep my hand on the chaises. Although, I built my PC in May and the humidity is higher than it is during the Winter.