The primary technical specs of the Qualcomm Snapdragon 820 are available from the company, and everything we know indicates that it will NOT have the same overheating problems as the Snapdragon 810. The main difference that supports this assumption is that it will be built on a 14nm FinFET fabrication technology designed by Samsung and GlobalFoundries. This smaller manufacturing process means the chipset will consumer less power and output far less heat than the 810 chip.
On top of this, Qualcomm will be introducing its new Kryo microarchitecture with the 820 chipset. In fact, engineers and developers within the industry are pretty excited about the new direction that Qualcomm is taking with the 820 and believe it could be one of the fastest and most powerful mobile chips ever designed. Of course, a massive success is exactly what is needed by Qualcomm to get them back in the game after the disaster created by the Snapdragon 810.
Here's a lengthy writeup over at PhoneArena that details what is known about the Snapdragon 820 at this time: The Qualcomm Snapdragon 820 everything we know and what we expect