Do you know what fibres and dyes were used in making the rugs? What might the action of heat be on them? As the fibres and dyes age they will become more susceptible to odication, cross-linking and chemical deterioration – many of these reactions are accelerated by the energy provided by heat. What effect will the heat have on substances which have become ingrained in the rugs over time – spills, stains, dust particles ? Some of these will become insoluble as a result of heat action. In many cases the rugs will have been made from wool (there don’t seem to be many survivals from plant fibres) – a protein based fibre made mostly of amino acids with a complex structure which controls its elasticity and shape. Applying heat will pernanently affect these fibres. Then add to this complex arrangement, the effects of the dyeing and treatment the fibres have already experienced and the effects of age. You may not see any immediate damage, but the fibres in the areas treated are likely to become more fragile and deteriorate more quickly. They have already suffered from being folded without padding,. forming the creases you mention.