if he were having an allergic reaction to it, it would be where his body is contacting the fabric (I know this as back when the Regent came out, some kids were allergic to the dyes used in the Sahara Fabric)
Can you put back on the cowmoo and see if it happens in that cover?
even though it may not be THAT hot, it's still hot out and everyone feels temps differently... which is why my daughter can literally spend all day out in 88* heat comfortable in long sleeves and long jeans... but her brother is dripping sweat by the end of it and is usually not wearing a shirt... just a pair of shorts.
She starts feeling cold and NEEDS at least a hoodie, sweatshirt, or jacket if it is so much as 70*... he has gone to school in shorts and a t-shirt when it's only 50 out and been fine and not understood why I was frustrated that his father let him go to school like that (we got a note home that they were concerned he was underdressed)