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I'm not sure, but I think IFTTT is sposed to manage things like that, I've done similar things with my Alexa devices (I am super new to Nest, but know that IFTTT deffs has Google/Nest support). For example, I can control my desktop PC through Alexa commands via IFTTT...
I was also prompted to link up a 'Smart Things' app to the Nest Home account, which I havn't investigated, at surface level it seems like a simple version of IFTTT...
Again, not sure at all, but those 2 services might be worth checking out if Google doesn't do it natively.