As you are feeding small meals, one possible cause is the milk is getting into the wrong stomach due incorrect feeding technique. I see lots of people holding the lamb’s head right up with the neck nearly straight; this is incorrect. The lamb’s head should be only slightly above the horizontal. The milk needs to run down the oesophageal groove in the front of the gullet, this takes it directly into the abomasum which is the only place it should go.
From reading, it would seem that the warm milk thing is to do with bacteria multiplying faster in warm milk. So if the hygiene isn’t tip top, it’s probably better to feed cooler, as others have advised. And if the wrong bacteria are established in the abomasum, then again feeding cooler milk will slow their multiplication.