Just recirculating the quantity of water needed to fill the trenches would not make a sufficient difference. The water temperature would continue to lower in pace with the season.

What is required is a supply of water at a constant temperature, such as water from a large spring or spring fed stream.

Jim

Below is a link to a big government document, PDF. The Google snippet has parts of sentences about pumping water "for temperature control" and returning it.

Googling for irrigation and "for temperature control" pulls up about 12 thousand ghits. The link below is the only one on the first page where the snippet reads like what your are thinking about.

Here is a link that might be useful: Big dot gov PDF on irrigating for temperature control