Coconut milk will separate if it dips below 57.2 degrees ... In the same breath, cream of coconut (think Coco Lopez) is super ...

I have great trouble getting mine to separate at all ... The fat naturally floats on the top (just as cream floats on top of milk), and chilling would cause the fat to really firm up.

As fresh milk cannot be kept for more than a couple of days, unopened, most is treated before sale. The vast majority will be homogenised, to stop the cream from separating from the rest of the ...

If you're dairy-intolerant, coconut milk and cream are an excellent alternative to cows' milk in some cooked dishes (provided you like its quite strong coconut flavour).