Hot water in cold water outlets?

I now have hot water coming out of my cold water spouts in every faucet in my home. When you first turn on the cold water it runs hot for a minute or so, then start cooling. There was no event that started this, it just started after several years of no problems. I have 3 tank water heaters. I have replaced all of the mixing valves in the house: two showers, one tub, & kitchen sink. All the other faucets are separate valves for hot and cold. I have shut off the water to the washing machine, and that does not solve the problem. I have looped the cold water feed lines into each water heater to try to create a heat trap. I have placed check valves on the cold water intake side of each water heater to try and keep the water from back flowing. Nothing solves the problem.
Any ideas?

Do you have water circulating line on any of your water heaters?

Do you have any hand held showers?

Terry is right, you are getting crossover some place. A pair of valves or faucets with hot and cold both turned on and a hose with a shut off. Check the basement or a dog washing shower. Something with a hose or something that can crossover.
Turned out she had washed the dog and left the valves on and turned off the hand held shower in the basement shower close to the water heater and was getting crossover, my dad felt sorry and didn't charge her. I would have.

That what would be called a bypass.

Thanks for you suggestions. I do not have a hot water recirculating pump. No hand held showers either. I have replaced the mixing valves in my master shower, upstairs shower, upstairs bath, & kitchen sink. All other plumbing is separate hot & cold valves. I have also checked the washing machine, by turning off the supply, so that is not it. I guess one of the replacement mixing valves could have been bad? No plumbing changes have been made, so no chance of cross connects. This problem just suddenly occurred, not as a result of any plumbing changes. Any ideas on how to verify if a mixing valve is functioning without having to add a valve to the supply lines? Could it be a problem in one of my water heaters? They are only a couple of years old, GE high end models, gas fired 50 gallons. Thanks.

I've started adding flow checks to mixing valves,tempering valves, you would have to isolate a mixing valve to see if it is causing a problem a valve is a good idea. You could try adjusting it all the way hot, or cold which ever you are adjusting.

You don't have a shower head with a shutoff and the valves on? Anything in the basement garage or shed?

Any faucet that has hot and cold turned on with a spout that turns off could be a problem. Some single handle valves can have a cartridge failure that can cause a cross connection. Another possibility is a hot water leak under the slab that heating the cold supply line. Are you on a slab foundation? Do you have a hot floor somewhere?