Temperature variation in the Arabian Sea area is a bit different as you can see in the Climate Explorer plot above. The summer peak monthly temperature is about 2 C above the annual mean.
For a similar region in the tropical Atlantic, temperatures spend more time near the peak. While there are different heat transfer dynamics, the preferred temperatures are very similar.
Dahl and Oppo 2009 did a comparison of paleo temperature reconstructions for the Arabian Sea with time frames of 0, 8ka, 15ka and 20ka BP archived at NCDC-Indian Ocean.
Core Time Slices Latitude Longitude Water Depth, m
11KL 0,8,15,20 5deg. 23.40N 60deg. 15.10E 3859
18KL 0,8,15,20 1deg. 54.00N 67deg. 20.50E 3035
26KL 0,8,15,20 15deg. 30.90N 68deg. 45.60E 3776
36KL 0,8,15,20 17deg. 04.50N 69deg. 02.70E 2055
57KL 0,8,15,20 20deg. 54.50N 63deg. 07.30E 3422
74KL 0,8,15,20 14deg. 19.30N 57deg. 20.80E 3212
6GGC 0,8,15,20 17deg. 22.90N 58deg. 47.70E 3652
These are the cores I selected.
Compared to "global" surface temperatures both the Atlantic and Arabian Sea blocks correlate relatively well but combined they have a better average 30 year correlation. If you only had one location to choose from, the Northern Tropical Atlantic would be the one, but the Arabian block after 1930 is very close. That could be due to internal variability and/or limited Arabian Sea SST data.
A problem though is that the available Indian Ocean temperature reconstructions don't correlate with each other very well. The Herbert et al 2010 core ODP722 has the longest time frame, but the others have much more variability during glacial periods. Dating between Bard2003 and Herbert2010 looks like an issue and the warm pool recons, Oppo2009 and Mohatadi2010 just have less variability. Still the overall uncertainty for the overlapping periods is in the +/- 2 C range.
The Mahtadi et al. 2010 used in the Marcott et al. 2013 holocene reconstruction with the Oppo et al 2009 "cap" appears to be a good reconstruction for the warm pool.
Since the Herbert et al 2010 Arabian Sea reconstructions ends around 7ka BP, the warm pool would provide an upper range plus extend the reconstruction to present.
So this would roughly be the summer SST in the Indian Ocean for 1 million years +/- about a degree. Average temperatures would have a larger range of around +1 to -2.5 degrees. Since most of the uncertainty is during inter-glacials I can add Bard2003 and Saraswat2005 for a more general Indian Ocean reconstruction.
This reconstruction will never fly without a lot more attention to detail, but it provides a rough idea of past temperatures with a little more realistic look at uncertainty, in my opinion anyway.
Since there is a gap in the Atlantic reconstruction and issues with the eastern Pacific there is only so much can be done.
Combining what I have so far with equatorial solar by Berger it appears that glacial/interglacial transitions only have about +/-1 C impact on peak tropical SST when there is enough data to fill in the gaps.