I'm not sure how he could get tangled in that... unless maybe if he chews on it or something? If you feel uncomfortable with leaving the sweater on, how about giving him a blanket for him to burrow in? That's what Zoey usually does. And then when the heat comes on, she'll lay on top of the vent.
Do you know if Bentley prefers warmer or cooler temp? Magnus for most part likes the cooler weather so I don't put a sweater on him if it's like 70. Zoey would shiver in that temp so I put a sweater on her or wrap her up like a burrito when we go out.