My research and understanding is that fresh milk actually does come out of the breast warm at right around core body temperature. It can feel cooler when you hand‑express because the moment it hits the air or your hands then it loses heat really quickly as your skin is much cooler than your core, so the contrast can make it seem like it’s room temperature even though it wasn’t when it left the breast.
Breast milk is also full of HMOs and other bioactive components that start breaking down once they’re exposed to air, which is one of the reasons feeding straight from the breast offers benefits a bottle can’t fully replicate.
So your experience makes total sense but the science is pretty consistent in that milk starts warm and it cools fast once it’s expressed and many of its goodies are at their best right at the source.