I plan to do approximately a 1'x1' curved ditch between my garden rows filled with wood chips, and manure, will this make the plants get too warm, or will it keep the soil cooler like cover crops do??
If you are talking about making heat from compost decomposing between your beds whether you are in a green house or out of doors you won't be able to use that heat nor should you. The heat will not 'improve' growth or enhance production. Too unpredictable as a heat source. Are you thinking to lengthen the growing season one end or the other of the growing season? Perhaps in conjunction with row cloth?
Cover crops do not make the soil cooler. They provide a bit of shade that blocks light inhibiting the germination of weed seeds. Weeds have a more difficult time becoming entrenched when cover crops occupy the bed for the winter. Cover crops are annuals meant to produce flower and seed in the spring. Do not allow them to make flowers or go to seed. They are meant to be 'green' compost, break up the soil with their roots and inhibit weeds during the winter. In the early spring, before the cover crop is able to flower, you knock them down and chop chop with the shovel, I also add a little bit of Nitrogen, clean out my trenches beside my raised beds, throw the soil onto the bed...
In a month or two that cover crop will be mostly decomposed, you should be able to plant seeds or starts. That decomposed organic matter is to feed the micro and macro organisms of your soil. This is in no way meant for fertilizer, even if legume.
Decomposers need nitrogen to do their work. When the cover crop has had a bit of time being decomposed by decomposers using the nitrogen you added to hasten the process, that soil will be aerated, warmed by biological activity and ready for planting seeds or starts.
You still have to add a bit of balanced fertilizer for your plants. No question about that.
Cover crops add organic matter and greatly add to the TILTH of your soil. They do not add chemistry plants have to have to do photosynthesis. The cover crop needs a month or two to decompose before planting that row. Only use a shovel if you have clay and/or wet soil. No rototiller.
I've watched 6' piles of bark chips create clouds of fog all winter. To become 6 inches deep by spring. There are far better ways to heat a greenhouse. There is no way to heat the vegey garden out of doors. Row cloth all by itself boosts the temp below the row cloth by 10 to 20 degrees. That would be your only choice to increase the warmth of the soil, well, that and double digging to make a raised bed (no lumber, brick, rocks...).
Decomposed organic matter spread on the top of the bed in between plants inhibits weeds, feeds the soil (organisms), who build up your soil, mix this organic matter into your soil FOR you. This activity warms your soil, adds air and drainage...this will never replace fertilizer.
Not enough room i/n my greenhouse to warrant decomposing organic matter especially to use as a heat source. I like keeping compost away from my garden as it attracts wildlife and rodents. The heat created is not stable enough to maintain consistent temperatures. Way too iffy of a system to ensure plant health.
Heat at odd times will cause plants to think they are in spring. They will start putting out tender growth to get ready for spring. One day or night your compost is unable to keep the ambient temperatures above 50 degrees Fahrenheit (assuming you are in a greenhouse), plants freeze, die, organisms go dormant..
Are you growing out of doors? Greenhouse? What are your goals? What did you like about this heat from decomposition? Where is it that you live?