It could not hurt to ask the doctor, but it would require a careful evaluation to tell the difference between typical skin temperature and something unusual. Kids hands and feet can get cold pretty quickly, when they are moving around, and almost every kid is different.

If a child has constantly cold hands, that could be a sign of a separate problem, such as anemia, diabetes, Buerger's disease, or even peripheral artery disease. If he had diabetes, though, you might have already noticed other symptoms.

He could have Raynaud's, which is a blood flow condition that causes fingers to get cold (and numb), but is not particularly dangerous.

There are a wide variety of body temperature patterns that all fall within the "normal" range, though, which makes them less useful for diagnosing GI problems.

If you suspect GI problems because of frequent constipation or diarrhea, it is definitely worth the trouble to talk to a specialist to find out what they can do. Younger kids with ASD may not be "in touch" with their body enough to tell you that they are in pain.

But if they are in pain, you will see a clear improvement in symptoms when the pain is eliminated.

Hypothyroidism can cause cold hands and feet.
Most autistic children are sensitive to gluten. They make antibodies against the gluten, but those antibodies also attack THYROID. So gluten free diet improves hypothyroid symptoms.