I think you're mistaking the lack of evidence for the actuality of absence. But most relicts don't survive. Stone tools a durable, but wood and fiber aren't.
Also, even at maximal glaciation there were large areas that were temperate. Many of them are currently under water, so we really haven't even looked at them.
Additionally, technologies take time to develop. With relatively small populations, the development is slower. There is probably a minimum population size that is required for each degree of technological development, since you start to need specialists. (We know that at least one quite small group in the old stone age had a specialist in pottery, but most of the evidence for other specialties isn't as durable.)
So your assertion that earlier civilizations required the earth warming up is to definite and too sweeping. It's plausible, but to go further is to go beyond the evidence.