It's tough to see anything as the board gets close to the case. I've been trying to figure out what to use as well. I used a small piece of play-doh on the CPU and compressed it when closing the case, and from that compression thickness I'm guessing the gap is less than a 0.5 mm, so some thermal paste maybe the way to go, or at least a compressed 0.5mm thermal pad.
I have the rev3 case and just picked up the RP 3B+. I think the issue is that the CPU in the new model is maybe 1-1.5mm taller than the 3B. So the new Pi will fit in the FLIRC, but I bet the thermal pad will need to be thinner. From poking around, it looks like the current pad is 1.5mm, so I'm guessing a thermal pad around 0.5-1.0mm would be better to minimize compression. Here are pics for the 3B and 3B+ from www.raspberrypi.org.