I dont see a problem with having a 4x2x2 enclosure. Yes, its more area to heat, but the BPs actually stretch out if they're given the space. Plus, it's going to be easier to clean. I guess height is personal preference. If you do decide to go with a 4x2x2, you won't be stressing out your BP. Just make sure to provide some fake plants so they have some cover.
Yes, the Hydrofarm thermostat will work to regulate the heat tape. Make sure to secure the heat tape outside the enclosure.
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