In hot weather, hanging baskets will probably need watering at least once a day, potentially twice during heatwaves which are becoming more and more frequent nowadays.
The reason for this is because hanging baskets contain only a small amount of compost, so there is less moisture available for plants to draw from. Especially if they are exposed to sunlight and wind, this will cause water to evaporate even quicker.
If plants are flowering they can also be extremely thirsty so they will need regular watering to support growth.
Throughout summer it's good to get in the habit of checking your baskets each morning. Water generously until you see excess water beginning to drain from the bottom of the basket. This helps ensure the moisture reaches the full root system rather than just wetting the surface.
During really hot spells like heat waves, check them again in the late afternoon or early evening. If the compost has dried out again, they may need watering again.
You can actually check if your hanging basket needs watering by lifting it carefully and seeing if it is lighter than usual. This will be a sign that it's lost a significant amount of moisture and might need watering again.
 

Rather than there being a particular temperature that hanging baskets need to be watered at. It makes sense to think more about weather conditions instead, but as a general guide:

• Below 18°C: Check regularly and water when the compost feels dry.
• 18–22°C: You may need to water every one to two days, depending on sun and wind.
• 22–28°C: Daily watering is often necessary, particularly for baskets in sunny positions.
• 28°C+: Hanging baskets may need watering both morning and evening.

These are just guidelines however.
For example, a sunny, breezy day at 21°C can dry out a hanging basket faster than a cloudy, still day at 25°C. Wind is particularly important because it increases evaporation from the surface of the compost and the foliage.
The size of your basket also has an impact. Larger baskets with plenty of compost will generally retain moisture for longer than a small basket packed with flowering plants.
The best approach is therefore to check the compost in each basket individually.

Pushing your finger around 2–3cm into the compost is the easiest way to check.
If it feels dry at that depth, it needs watering. If the compost still feels cool and moist, you can usually leave it for a little longer and check again later.
Don’t just go by the top soil appearance as the top layer can look dry while there is still plenty of moisture underneath, particularly after watering.
Look at the plants too, if you have wilting leaves and flowers this can be an obvious sign that they're thirsty, although it's advisable to avoid getting to this stage before watering.
If your basket is repeatedly wilting by the end of the day, it may be a sign that it needs more frequent watering or that the plants are receiving too much direct sun.

Early morning is generally the best time to water hanging baskets, when temperatures are cooler, causing less water to get lost immediately through evaporation. It also supplies the plants throughout the day when they're actively photosynthesising and transpiring.

In periods of extreme heat it’s advisable to check your baskets again in the late afternoon or early evening as they may need a top up.

Don’t water during the hottest part of the day as you’ll find a lot of the water will evaporate before it has reached the roots.

The short answer is yes, give the basket a thorough soak, water draining from the bottom is the clearest sign that moisture has travelled through the compost and reached the lower part of the root system which is exactly what you need.
Don't go overboard and keep watering until it is saturated. You just want to moisten the compost and then allow excess water to drain away.
If water immediately runs through the basket without soaking into the compost, the growing medium may have become extremely dry and water-repellent. In this situation, watering slowly and gradually can help the compost absorb moisture more effectively.

You can definitely over saturate a hanging basket.
This is likely to happen when drainage is poor and excess water is unable to escape. If you overwater a hanging basket the roots can remain saturated for too long, reducing the amount of oxygen available around them.
Check there are no things blocking drainage holes, such as saucers, trays, or liners, as this can also lead to over-watering.
Signs of overwatering include yellowing leaves, limp stems despite the compost being wet, mould or algae on the surface and an unpleasant, sour smell.
In severe cases, plants can develop root rot.
The key is to soak thoroughly, allow excess water to drain away and then let the compost dry slightly before watering again.

Generally, yes, this is due to plants growing in the ground having access to a much larger volume of soil, which retains moisture around their roots. Hanging baskets have access to a  much smaller reservoir of compost so they need more tending to.
Being exposed to air on all sides rather than surrounded by soil also means hanging baskets need more watering.
This is why you need separate watering routines for your borders as well as your hanging baskets.

There are several simple ways to reduce how quickly your baskets dry out.
Start by choosing a good quality, moisture retentive compost when planting and consider adding water retaining material where appropriate. Don't overcrowd the basket either. Although a densely planted basket can look good, too many plants competing for a limited amount of moisture can make watering more demanding.
Positioning also matters. Hanging baskets in full sun will generally need more frequent watering than those receiving partial shade.
If you're going away during the summer, consider installing a simple drip irrigation system or asking someone to water your baskets regularly. This is particularly important during hot weather, when even a day or two without water can leave smaller baskets severely dehydrated.

There's no perfect watering schedule that applies to every hanging basket. The most reliable approach is to monitor the compost and adjust your routine according to the weather.
As temperatures rise, check your baskets more frequently, particularly during periods of sunshine and strong winds. Water deeply in the morning, check again later on very hot days and always make sure excess water can drain away.
With a little regular attention, your hanging baskets should reward you with healthy foliage and plenty of colourful flowers throughout the summer.