A paper in this week's Nature uses climate modeling to determine when future expected high temperatures will be outside of the range of historical high temperatures for the modern instrumental period and suggests that it could be 20-50 years from today.
A group of researchers from Hawai'i and Japan took climate models extending out to 2100 and determined how the climate models expected near-surface air and sea surface temperatures to change around the globe. They then checked these expected values, at annual and monthly levels, against previous climatic records to determine when the mean temperature in an area would be outside of the bounds of the observed historical variability from 1860 to 2005. To account for variability in climatic response to differing levels of carbon forcing, two climate models were used: one assumed "business-as-usual", another assumed the some forms of carbon reduction were put into place.
"We found that the year at which the climate exceeds the bounds of historical variability depended on the modelled scenario. Under RCP45, the projected near-surface air temperature of the average location on Earth will move beyond historical variability by 2069 (±18 years s.d.) and two decades earlier under RCP85 (that is, 2047 (±14 years s.d.)."
Monthly climate departure dates lag behind annual climate departure dates: the paper forecasts that, globally, every year will be warmer than 1860-2005 by 2047 ±14 years, but every individual month won't be hotter than its comparable month between 1860-2005 until about 2090.
The paper, since it focuses on forecasting climate variability at regional and global levels, also discusses when biodiversity hotspots can expect to see their climate departure date. In short: they generally get these changes before the rest of the world does, except for marine birds, whose biodiversity hotspots won't be affected for a little bit behind the global average.
All in all it looks like a very exciting 21st century we have planned. If looking for a less technical write-up than the Nature paper itself, try this by the New York Times.