Wow, what a confusion.
Actually, when you "turn" through a wind field/direction, you get "blown" away. This blowing away, will take care, the wind will increase your kinetic energy. Though, this is not instantly. Have a heavy airplane with a lot of wind, and it may take enough time to get a stall surprise.
On a base leg, you will need to turn a little into the wind, to avoid, your base leg (ground track) is not perpendicular to the runway. When you start turning, your airplane starts to get caught by the wind and accelerated in the direction of the wind. Be heavy and turn fast, the wind does not have sufficient time to accelerate the airplane and the airspeed will drop. Have a light airplane, and the wind will accelerate the airplane within a few seconds.
For the example to make 360 turns in a steady wind, it is not defined, whether the circle should be ground based or relative to the (moving) air. With a ground based circle, you will have a constant kinetic energy, though juggling with the power (and varying airspeed) to make it a circle on the ground.
With a moving air circle, your airspeed will remain the same, though because your ground speed will continuously vary, the kinetic energy will continuously vary. To accomplish this, you will need to juggle with the power setting. The moment you turn "into the wind", you will need to bleed off ground speed, to avoid your airspeed going up (IE you will need a little less engine power at that moment). And the other way around.
Oh, and I fly and a often windy airport, where multiple 360s due to other traffic are pretty common. And flying a nice 360 ground based requires a constant power setting / trim juggle. Often, the 360s tend to become ovals.