Control climate and media_player locally with Alexa

Hello there!
I managed to control smart lights with Alexa locally (i.e. without exposing my home assistant) using the emulated_hue integration. Alexa does discover the lights locally and can control them without accessing the internet.
I want to do the same with the media_player and climate entities, i know emulated_hue allows partial control for media player like volume with brightness and things but it is weird to say “Alexa, set the brightness of the TV to 50%”. Anyway, it is surely not doable for an air conditioning unit witch has tons of modes.
Any ideas?

I already tested the aws lambda solution and it works. Now I’m trying to convert to a local setup.