Is there a scientific consensus on a model that accurately predicts the magnitude of global warming (assuming no policy interventions to reduce CO₂ emissions) over a given time span?

Is there scientific consensus on a model? 
Yes.

This is precisely what the IPCC report on.
Fifth Assessment Report - Climate Change 2013

This includes a whole chapter discussing modelling techniques and assessing their accuracy.

You can see that the models have been good at predicting temperature until the last few years, with the famous "hiatus" in air temperatures. Measured temperatures have been at the bottom end of predictions (but despite some people's impressions not below the predicted area, and temperaturews have not returned to normal).

There is a huge amount of research around how to improve the models, and to understnd what factors have led to the "hiatus". 

Wikipedia intro to climate modelling  Climate model

Climate models on the web

• CMIP: Coupled Model Intercomparison Project
• NCAR/CESM: Community Climate System Model (CCSM)
• NASA/GISS: NASA Goddard Institute for Space Studies
• EDGCM/NASA: Educational Global Climate Modeling
• climateprediction.net, community climate prediction