I have a MacBook Pro (Retina, 15-inch, Mid 2015) with both discrete (AMD Radeon R9 M370X) and integrated (Intel Iris Pro) graphics. When this machine is connected to an external display, I find that the keyboard gets uncomfortably hot even when doing very light work, and it gets annoyingly hot when doing anything heavier like compiling code.
I know that attaching an external display forces use of the discrete graphics adapter because the HDMI port and DisplayPort are hard-wired to that adapter. Unplugging the external monitor brings temperatures reported by the sensors down, and subjectively brings the keyboard back to "body temperature warm" instead of "annoyingly hot". A drop in temperature is observable even when the discrete graphics remain in use but only the external monitor is disconnected.
I can see why the graphics processor uses more power and creates more heat when driving multiple displays, but my question is the following: does the equivalent machine with only integrated graphics show the same magnitude of heat increase when using an external monitor? Presumably the integrated Iris graphics will also get hotter when driving multiple displays, but will it get this much hotter?
I don't have an Iris-only model around to compare, so I will supply some measurements from iStat Menus, and hopefully someone with the Iris-only config can take equivalent measurements. I will report the "left fin stack" and "CPU PECI die" temperatures, which react quite visibly to the use of an external monitor. All temperatures are measured with very low CPU activity, with any open applications essentially idling.
With a 1920x1080 display connected in a room climate controlled to a temperature of 25C, the left fin stack (LFS) is 51C and the CPU is 61C. A few minutes after disconnecting the display, LFS is 40C and CPU is 49C. After plugging the external monitor back in for a few minutes, LFS rises back up to 52C and CPU to 62C. The fans remained at around 2000RPM throughout the measurement process. So put simply, I get around a 10C increase in LFS and CPU temperature purely from plugging in an external monitor via HDMI.
The LFS temperature as reported in iStat Menus shows a nice smooth exponential rise and fall as one would expect: 
Thanks in advance to anyone who can supply the other half of the information needed to answer this question!