It's not the temperature it's the pipes that carry hot and cold water are different pipes and they can give or take minerals. Test kits can be found a Walmart, pool supply stores, hardware stores, pet stores, and online. You'll need to make sure the kit says it tests for Total Hardness or General Hardness and has a scale that goes to at least 250ppm. Testing water directly from the machine is best. If you plan to use hot water to wash, both hot and cold should be tested. ** Avoid the free Whirlpool and Water Boss brand tests as they have been known to give inaccurate results. Also, avoid the electric TDS tests as they do not test Hardness.
If you have a Petsmart nearby they test water samples for free. Canada Home Hardware tests for free, as well.
If you don't want to search for a kit, here's one you can order from Amazon
If you're using tide free and gentle and your water hardness number is 0-100ppm you don't need additional water softener for diapers.
If you're using tide free and gentle and your water hardness number is 101-180ppm you need 1/2 cup borax OR a cap of calgon OR 3/4-1cup washing soda in the mainwash only.
If you're using tide free and gentle and your water hardness number is 180-250ppm you need 1/4 cup borax OR a half cap of calgon OR 1/2 cup washing soda in the prewash AND 1/2 cup borax OR a cap of calgon OR 3/4-1cup washing soda in the mainwash.
If you're using tide free and gentle and your water hardness number is 250ppm or more you need 1/2 cup borax OR a cap of calgon OR 3/4-1cup washing soda in both washes.