My Keurig K latte doesn't froth or heat milk?

SOURCE: Aeroccino part for warming milk

you should contact nespresso to buy a new one.
www.nespresso.com

SOURCE: milk not frothing

Remove the black plastic outer sleeve of the Frothing Wand (some models have a metal outer sleeve). If done correctly, the “sleeve” has been removed, but the inner wand with red or black washer, is still connected to the machine.
2) The part of the sleeve assembly that you have removed is comprised of 2 pieces, the frothing sleeve and the center piece. The center piece can be seen if you look into the top of the wand.
3) Using a pencil (eraser end), or similar shaped object, push down on the center piece until an audible “click” is heard. The “click” means that the centerpiece is back into the proper position. When in the proper position, the center piece visibly sticks out the bottom of the sleeve about ¼-inch. It looks like a bird beak.
4) Now put the sleeve back on the machine and your machine should be ready to froth again.

As for the milk island, translaltion from the italian solution using google and drying all the parts works

SOURCE: the steam wand is bubbling the milk, not frothing

THere is a little black tube inside - make sure its pushed out enough - about 1/16 an inch from the bottom. And you may have to clean it out. Happens to us too and after I do the above it works

Testimonial: "Thank you very much for the advice. I adjusted the black tube and the frothing is back!"

SOURCE: My Nespresso milk frother did not come with

they make one that has the option of frothing milk hot or cold. Blue light is cold. Red light is hot. The red light will always heat the milk. To get to the blue light, you need to hit the button twice.( First will go to red)

SOURCE: the milk doesnt heat up

We had the same problem with burn marks on the bottom and flashing red light etc. Now we just rinse the container out with cold water each time we use it - do not dry, just leave it wet and then add your milk. Heats up perfectly each time. The water lubricates the base of the container, preventing burning. Nice hot coffee every time now. Hope this works for you too!