Can you make whipped cream with coconut milk of the milk is not chilled?

Another helpful hint is to "freeze" your metal mixing bowl and whisk beaters for 5-15 minutes. Really helps.

Interesting question. I would wonder if you're talking "coconut milk" or "coconut Creme".
The creme product is normally found in the mix drink section for making mixed drinks, with a high fat and sweetness and rather homogeneous.
The "milk" can sometimes be a little iffy on the fat content, some brands don't have the fat disk, others do.

It works best when the coconut milk is cold because you are only using the coconut cream that rises to the top when the coconut milk is chilled. Use a high quality coconut milk. I whip mine with some maple syrup and some high quality vanilla extract.