But I find that your answer is not completely clear to me, but I believe that you are saying that when loaded, ferrite cores are hotter THAN when there is no load. That is what I would expect.

Yes, that's what I mean.
sorry for saying it is unclear

 

Yes, that's what I mean.
sorry for saying it is unclear

OK then. One more simple check is for overall efficiency, which ought to be fairly high. You know the power out, and you should be able to measure the power in, volts times amps. So then efficiency is power out divided by power in.

Next, power in minus power out will tell how much power is being converted into heat, since presently there is no other way power can be consumed, except for a small amount radiated as electrical noise.
If it seems that the power heating the output transformer core is excessive then either adding more turns to each winding to maintain the voltage but reduce the magnetization, or using a larger core, are the reasonable options. It might also be that the supply is capable of more power output than your application requires.

And one more possibility, mentioned once already, is that the heating of the core is OK, just not expected. You did not mention how hot it gets and what temperature it stabilizes at, or if it just keeps getting hotter.

 

I experimented and found that: when loaded, ferrite cores are hotter when there is no load. And I really don't understand this phenomenon

The problem you're having is that there are too many things you don't yet understand (it takes time, it really does). In order to understand the core, you need to go learn why 'ferrite' is used. It has to do with it's feromagnetic properties by design.

 

Please share your solutions- so that others may learn from you.

 

I agree, it would be nice to know what you found and what you did about it.

If you would like to confirm the transformer function, why not ad some circuitry to scope the B-H sat curve during operation.

 

I using feedback to regulare output voltage.