The new 3B+ controls heat better than the old 3B model, but if you want to push it hard for extended periods at max performance (no thermal throttling), then some additional cooling might be needed. However, fans and heatsinks are not necessarily the best solution.
- The tiny heatsinks sold for use on the Pi are not very effective, especially since many of them are supplied with ordinary plastic tape (not thermal adhesive).
- Fans are noisy, require additional power, and over time they will fill your system with dust.
A better solution is the Flirc generation 2 case for the Raspberry Pi3B.
New shipments of the case now include a thinner thermal pad that allows it to fit the newer 3B+ model.
I've had one of my Pi3B computers in a Flirc since last November (2017), and I recently put my new 3B+ in the case pictured above. As you can see in the second picture the case has an internal post that makes contact with the SoC (CPU+GPU), so the whole upper shell of the case acts as a huge heatsink to keep your Pi cool without the noise or dust of a fan.
The only drawback to the Flirc is that the GPIO is not readily accessible. There is a slot in the bottom to pass GPIO connection wires out of the case, but if you are experimenting and frequently change GPIO connections it could be inconvenient. Common IDE type ribbon cables will not fit because the mounting holes are too close to the GPIO header, but "DuPont" style cables will work.
The Flirc Gen2 case for the Pi3B/3B+ is my favorite case (I've tried several different cases). It looks great, cools well, and isn't even all that expensive. I got my first one on a Lightning Deal for $11.95, and the one I bought recently was $15.95 (which is the normal price).
My mind is like a browser. 27 tabs are open, 9 aren't responding,
lots of pop-ups...and where is that annoying music coming from?