Are you referring to covering the soil with red plastic, or using mulch made out of wood that has been dyed red?
In either case, the advantage of the red color, rather than black or white, would be that red absorbs a lot of light, but reflects red, which is a part of the spectrum that plants can use and tends to promote flowering and fruiting, so you're giving a little boost in available light.
Either case would probably also tend to increase moisture in the soil. However, the plastic would probably heat up the soil more quickly than the wood mulch. The wood mulch might actually insulate the soil to some extent and keep it a bit cooler. It will soak up moisture when it rains or when watered, and when it is warmed by the sun it will give up this water via evaporation, thereby providing a cooling effect. The plastic would tend to work like a greenhouse and keep heat and moisture in.
The soil in the black, exposed pot will already be warmer in the summer and cooler in the winter than the ground itself. It is worth trying these methods, I think, but I would not expect it to be a game changer. Probably more useful would be to try to put next to south facing wall or some similar situation.
Rob