The climate models have been uncannily accurate

For what it's worth, any claims you may have heard that there is a gap between the major climate model projections for global temperature and actual observed temperatures are false.

In the chart below, a composite model of climate change projections is compared to four of the most widely-respected datasets of actual, measured, and globally averaged temperature measures:

UK Meteorological Office/Hadley Center's Climate Research Unit HadCRUT5

NOAA's National Centers for Environmental Information (NCEI)

NASA's Goddard Institute for Space Studies (GISS) GISTEMP 

Berkeley Earth http://berkeleyearth.org/

The black line on the chart is the Coupled Model Intercomparison Project phase 3 (CMIP3), which combines multiple projections/predictions into a single projection.  The gray area represents the area of 95% certainty around that single projection (essentially, it encompasses 95% of the variability in the various models, most of that variability is based on different scenarios for the future, such as population growth/decline, increase/reduction in the use of fossil fuels).  

Although neither is used in the chart, the datasets of both Japan's Meteorological Agency (JMA) and the EU's Copernicus Climate Change Service (C3S) are in close agreement with the others.

Climate models and projections of global warming have proven to be extremely reliable.