When using an external monitor, does a mid-2015 Retina Macbook Pro with only integrated graphics run cooler than one with discrete graphics?
The short answer appears to be: yes, 12 degrees C (22 degrees F) or more cooler. 

I got ahold of a custom-build Macbook Pro that has identical specifications except that it had no discrete graphics adapter. I set it up on the same table in the same room, connected to an identical monitor. I put both of them through the same sequence of operations, using yes &gt; /dev/null &amp; one or more times to occupy whole processor cores, running WebGL demos, plugging and unplugging monitors, etc. in lockstep. Temperatures, fan speeds, and CPU use were observed regularly using iStat menus, yielding 120 separate observations. Using the R statistical package I fit some models to these data and retained this one for the "left fin stack" temperature:

&gt; summary(fin_fit)

Call:
lm(formula = fin_temp ~ dgpu + ext_disp + cpu_load + gpu_load,
    data = heat)

Residuals:
     Min       1Q   Median       3Q      Max
-12.1091  -2.8460  -0.2888   2.5413  12.1540

Coefficients:
            Estimate Std. Error t value Pr(&gt;|t|)
(Intercept)  32.8460     0.7066  46.484  &lt; 2e-16 ***
dgpu         12.2631     0.8067  15.202  &lt; 2e-16 ***
ext_disp      2.4160     0.7836   3.083  0.00256 **
cpu_load      3.4386     0.4173   8.240 3.11e-13 ***
gpu_load     14.0506     1.2601  11.151  &lt; 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.138 on 115 degrees of freedom
Multiple R-squared:  0.821, Adjusted R-squared:  0.8148
F-statistic: 131.9 on 4 and 115 DF,  p-value: &lt; 2.2e-16


Interpretation: This model explains about 82% of the temperature variation. The base operating temperature is about 33C, every fully occupied CPU core adds about 3.4C, a fully occupied GPU adds about 14C, each external display attached adds about 2.4C, and using a discrete GPU adds about 12C. All of these variables are very significant in explaining temperature variations, and the model as a whole is quite effective at predicting temperature.

There is an apparent jump of 10 watts or more in power consumption when using the DGPU and an external monitor. This would be coherent with the extra heat, but I did not fit a model for this response variable.

I expect the fin heat model would fit even better if I excluded all observations that happened shortly after a change of state (change in CPU or GPU usage, change in presence of external monitor). There’s some amount of thermal inertia - it takes a minute for the heat sinks to warm up or cool down.



Conclusion: On the stock Macbook with a discrete graphics adapter hard-wired to the external monitor ports, from a temperature perspective attaching an external monitor has greater impact than performing heavy computations. The fans become audible frequently under load, and the keyboard can get uncomfortably hot. On the other hand, when using the model with no discrete GPU, the fans remain quieter and temperatures more moderate, as attaching an external monitor yields only a slight increase in base temperature.

Other observations: the dual-GPU model will also enter and remain stuck in discrete GPU mode when it doesn't really need high performance graphics, which can discharge the battery very quickly and cause unnecessary heat. At one point in my testing after unplugging the external monitor, it became stuck in DGPU mode. The activity monitor reported that this was due to the Terminal application requiring accelerated graphics (!). 

Coming out of sleep with a monitor attached or switching on an already-attached monitor, the monitor often seems not to be detected or used by the OS. GPU switching seems to add a lot of complexity and be susceptible to glitches.