How much does basement temperature affect a heat-pump water heater?

I’d lean toward the warmer space if the basement is already cool and shares air with living areas: extracting more heat there could make comfort a downside, even if the dehumidifying effect is welcome. If the basement is separate and tends to be damp, the dehumidifying effect might be a plus, though the cooling could still matter. I’d still compare the unit’s temperature limits and clearances before letting either preference decide the location.

Room volume affects how quickly the unit’s cooling becomes noticeable: a larger space generally buffers the effect better, while a small enclosed room may cool more and have less air available. Ducting can help when the room is too small or you want to draw from or discharge to a different area, but it doesn’t automatically solve every layout - check that the specific unit permits the proposed ducting and follow its airflow and clearance requirements.

When you mention drawing from or discharging to another area, would you prioritize routing the cool exhaust away from connected living space, or bringing intake air from a warmer area? Those solve different comfort concerns, and the useful option depends on what the particular unit permits.

If the main concern is keeping connected living areas comfortable, I’d prioritize sending the cool exhaust away from them. Bringing intake air from a warmer area may help with the source-air concern, but it doesn’t address where the cooled air ends up. Which matters more depends on the layout - and on whether the unit allows that duct arrangement.

Cooler source air generally gives the heat pump less heat to draw from, so a cool basement can reduce efficiency compared with a warmer utility space. How much it matters depends on how cool the basement gets and the specific unit; without those details, I wouldn’t put a number on the difference. A warmer location may therefore have an efficiency advantage, even if the basement’s other features make it more convenient.