If I want to tell someone that the temperature is going to increase over the period of night, how can I say that?
The temperature will increase during the night.
The temperature will increase throughout the night.
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"During" means within that time period, simultaneous with it.
"Throughout" means over the whole duration, from start to end. The action does not have to be continuous or constant, but it has to take place one or more times over the whole time period.
Note: in weather reports, meteorologists have a somewhat specialized jargon, and they often use "throughout" to mean "during; at any time between two points". Hence, in your example, there is no guarantee that they really mean the temperature will steadily increase the whole night, even though that would be the normal meaning.
Similarly, for space instead of time,
There were riots in the city
means in some places in the city, while
There were riots throughout the city
means more or less everywhere, in every neighbourhood.