Gen 3: 2007-2011 (UK 2008-2012) CR-V
I have a 2008 CRV, 2.4 L engine. It's a Mexican model..made and purchased in Mexico, where I live.
I've noticed that when I'm stuck in traffic for a while, the A/C seems to turn off until I get rolling again. No sign of the engine getting hotter.
This might be related to the cooling...