Nothing fringe about it, it's a general feature of inflation models. Exponential expansion essentially quick-freezes the universe, until the field which drives it (the inflaton) decays. At that point, exponential expansion stops (so no more cooling) and the universe fills with a hot soup of decay products. It's called reheating, and plays the role of old-school big bang:
https://en.wikipedia.org/wiki/Inflation_(cosmology)#Reheatin...