reference date time range, return the value into all cell that match datetime range

Hi Good people, Please correct or comment on any points to improve my posts.
I basically have sunrise sunset times and corresponding heat load for that day (call solar transmission table).

In another table I have hourly date time breakdowns for the whole year (call hourly solar capture table).

What I need to do is have the solar capture table look at its datetime and return the value from solar transmission that corresponds to the hours that fall between the range.

I have tried working around nested if and have done some array work but just cant sem to get the right combination.
In the attachment I have tried to show the output im looking for.
Date time lookup return value.xlsx


Some sturcture help would be appreciated.
Thanking you all in advance
BE WELL
JOSH

Thanks mlcb and alansidman
mlcb responce did the job,
alansidman also worked but I hade to flip the referecning likley due to my poor description in question
Both great structure reference as I go forward.
Thanks Again
Josh