Synthetic oil will reduce oil temperature but it's not a huge amount. It will not, in my experience and according to what I have studied, deliver a reduction in coolant temp that you can notice on a standard coolant temp gauge (like: "Wow! My coolant temp went down 20 degrees!").
My truck has separate oil and coolant temp gauges and I have been monitoring these things over several types of oil over the past few years. I did see about a 3-5 degree drop in my everyday running oil temp going from conventional 5W20 to synthetic (MC to RP) . I also saw a 5-10 degree rise in running oil temp going from the synthetic 5W20 to a mineral 10W30 (RP to MC HDEO). By "running oil temp" I mean the stabilized oil temp over a measured course with a measured load. That exact temp varies according to ambient temp and engine load but I know the variables now and have a baseline. In any of these cases, I do not see lower or higher coolant temps (on a very accurate Isspro stepper type gauge). With a large drop in oil temp, you probably would see a drop in coolant temp.
Also, I think the amount of the reduction in friction(and temp) from syn to conventional would depend of the amount and type of FM's used in the conventional oil to meet that "Energy Conserving" standard. I think with enough FMs in a good mineral base oil, it could really mimic a syn that wasn't FM'ed. Being additives, the FMs will eventually degrade while the syn base oil would retain those "slippery" characteristics more or less permanently. And then, you may have FM'ed syn oil. There are differences in FMs and how long they last but I don't know exact details
IMO, a small reduction of oil temp doesn't transfer to anything noticeable on the coolant temp side in normal situations. It does reduce the overall cooling system load a little and in extreme situations, you may see something noticeable but it wouldn't be much. I see it as one of the bennies you get with a good syn but by iteself, it's not all that significant for most of us.
You can see more of a temp reduction with gear oils, in my experience. Going from a mineral (usually Gp 1 or II) to a syn (PAO) delivered a 15 degree drop in oil temp over a measured course and with a specific load in each case, and with identical ambient temps.