A circulation pump for hot water. Yes or No?

It also depends on the overall system, for example how large the storage tank actually is. 40 degrees would not work for us because we have an integrated storage tank (170l). It runs at 45 degrees with a 5-degree hysteresis. If I set it to 40 degrees with, for example, 2-degree hysteresis, I wouldn’t be able to fill a bathtub with warm water, and the heat pump would constantly start/cycle for hot water and only run briefly.
As a rule, we have two cycles for hot water per day.

What is more efficient? No idea.
Fewer cycles lead to less wear and tear. With high investment costs, that’s more important than optimizing consumption costs to the last cent, I think. The principle of a small storage tank has worked well for us so far. A legionella program is not needed with this turnover, storage losses are lower.
But it’s hard to evaluate due to lack of comparison.

How have the heat pump users among you actually set up the hot water preparation? Do you let the heat pump prepare hot water once or twice a day to a higher temperature than delivered, or do you set e.g. 40° and then let the heat pump prepare hot water on demand throughout the day?

I only ask because at the moment with us it is like this: we heat the hot water storage to 50° even though we only draw 40° (via fresh water), but heating is only allowed once a day at midday (because of photovoltaics). Sometimes the storage is empty before the next heating phase... but unfortunately I haven't found a suitable schedule for us yet.

Hot water is made here between 11:00 and 17:00. Also because of the photovoltaic system. Normally, one hot water preparation per day is sufficient. It is set to 44°C with an 8°C hysteresis (fixed value of the heat pump) with a nominal volume of 260 l. But without a fresh water station. When only I shower, sometimes hot water is not made every day. Some fine-tuning is probably still needed here. So far, the temperature sensor is in the middle of the hot water tank.

44/8 surprises me a bit, as the hot water preparation only starts at 36. That is already too cold for showering/bathing. You can certainly still tune that, since you store a relatively large amount of very hot hot water.

Do you let the heat pump prepare hot water to a higher temperature than delivered only once or twice a day, or do you set, for example, 40° and let the heat pump prepare hot water as needed throughout the day?

Once daily in the early afternoon (photovoltaics + higher outside temperature) at 43°. 2-3 times a year it gets tight, then we press the button ourselves. We only shower in the morning.

If continuous higher hot water demand is no longer sufficient, I would increase the temperature to about 50° to only have to charge once. If even higher temperatures were necessary, I would charge twice at a lower temperature.

If comfort is everything, then always, nice and warm with a higher switch-on hysteresis to prevent frequent cycling.

We didn’t want circulation and planned accordingly. Charging once daily at a lower temperature would not work with circulation in our case. In the kitchen, the water could be warmer; there you could consider an instantaneous water heater instead of stressing the heat pump just for the kitchen.

We have now decided on circulation. The pump will have NO timer. It has a power consumption of a maximum of 5 watts according to the datasheet. Therefore, it will not cause more than 11-12€ per year in electricity costs if it runs 24 hours.

For an additional 300€, I think we made the right choice to go with circulation. It will be a great luxury that one will surely get used to quickly.

Not the costs for the pump can be high, but the heat losses through the water. Yes, they stay in the house, but in a very uneconomical way. If the heat generator constantly runs at 50 degrees, it simply costs.