I think it's important that you cool down in an extended state. If you are hanging, place the cool cloth on while still in the hanger with weights on. Same thing for pumping or any other exercise you want to cool the tissue while it is in an elongated state. This encourages the tissue fibers to remain that way. Otherwise, it may be counter-productive if you cool while turtled.
Notice what this article says (I posted it in another thread but here it is again):
Lehman and associates (1970) studied the effects of heat and stretching on rat tail tendons.6 The results indicated that heating alone produced no significant elongation and that stretching alone produced no residual elongation. Significant elongation occurred if heat and stretch were combined. A greater increase in length was maintained if the stretch was held during the period of cooling since “reorganization of the tissues is thought to occur during the cooling period.”6 Overall, the most effective method of producing a plastic deformation of connective tissue was to apply a sustained stretch during the application of heat and to maintain the stretch during the period of cooling. (Italics and underlines mine)
For the full article:
Heat Application in Physiotherapy
I found this while on my decon break so I haven't tried it. But you can bet I will.