You’re right that the sensory system of a fetus is developing in the final trimester. However, the fetus is floating in fluid inside the amniotic sac, which is inside the mother’s uterus. The placenta is in there too. The uterus is inside the mother’s abdomen, which has layers of connective tissue, muscle, fat, and skin. I doubt the fetus could feel anything like a bumpy cloth the mother was wearing.

Our bodies are good at regulating our temperature, so the temperature inside the amniotic sac probably doesn’t change at all, whether the mom has a heating pad or a bag of ice on her belly. The mother should just try to stay comfortable at a very uncomfortable time.

The fetus can hear in the third trimester. As their ears develop, they can probably hear their mother’s heartbeat, her intestinal sounds, and maybe blood flow. Sounds like the mother’s voice and external sounds would be distorted because the fetus is under water. Think about how things sound when your head is underwater in a pool or a bathtub. Some people think that providing music is helpful to the fetus. Some scientific studies seem to support that. Babies born prematurely may also benefit from music.

Do you think the kind of music would make a difference?

I am not aware if soft bumps or contact with the abdomen has been investigated, but I see no reason why it would. I am not sure that "we agree that a lot of external sensory development is happening."

Are you referring to the fetus or the mother? I'll assume the fetus. The fetus hears sounds, and there is information about that. Otherwise, the fetus is not likely to be affected much by things in contact with the abdomen. Here's some info:

How protected is the baby in the womb? In general, women’s bodies are not fragile. Historically, women have worked hard on farms and in factories throughout their pregnancies. Many still do today.

The uterus is a muscular organ that protects the baby from the jostling and bouncing of mom’s day-to-day. When combined with the shock absorbers of the amniotic fluid and the weight you gain during pregnancy, your baby is padded from the effects of most daily abdominal contact. Abdominal trauma is different. Vehicle accidents, falls, and overzealous lifting can be forceful enough to harm the baby. However, you can take precautions to reduce the risk of abdominal trauma, which we’ll outline here.

Here's info about when the fetus hears sounds outside the womb. The link has some interesting info:

When can fetus hear external sounds?
By week 18 of pregnancy, your baby's ear is well enough developed to start detecting noises. Around weeks 27 to 30, babies can turn their heads or otherwise respond to sounds they hear outside the womb.