Thank you Sinzia.
I watched a youtube video about re-seating cpu coolers, so I changed the entire block orientation so that the push-pull fans are oriented so that air flow is from the bottom of the case to the top. It is an 800D, so it has plenty of exhaust ports at the top.
I also redid the TIM, by applying a pea sized amount and then spreading it out with some thick paper over the top of the CPU.
Now, according to the Realtemp 3.60, the highest temperature my CPU attained during 10 runs of IntelBurnTest 2.53 at standard stress level on all CPU threads was 78 C / 172 F.
That temperature is so much better than the stock CPU cooler. Mind you, my parents like their electricity bill as low as practically possible, so that ambient air inside of the house is 24 C / 75 F.