I think the point of Coldwater Detergent is to use less energy by not using hot water. I think it would be as effective in hot water, but probably not more effective. Unless you have really dirty socks or ground in dirt, there would be no reason to use hot water.
Do you have something like Shout that is a stain remover? I use that to spray on grass stains, blood stains, ground in dirt, etc. I leave it overnight and then wash in hot water, if the fabric can take hot water and I always get the stain out.
I do have some stain removers, but they are a pain to use and often I forget to use them before the garment is washed and the stain is set. The problem is that my skin is very oily and so I want maximum cleaning action on everything by default.
Why not just pre-treat the clothes with the liquid Tide, and then wash in cold water. Works great for me. Even on tough stains and grime.
Just pour some of the Tide on the clothes and rub in before washing.
Cold or hot water makes no difference.
The Detergent will not be any more effective as it dissolves easily at low temps but the cleaning power of hot water compared to cold will be noticeable.
So Yes using cold water detergent with hot water will work better than cold, but its only the heat that gives the improvement.