At high temperature the mobility of ions increases. The excess mobility coupled with slight increase of CNT inner core opening promotes ingress of acid making easy removal of metal or other catalyst used during synthesis
acid treatment is one method to remove catalyst that have been used to synthesis CNTs. At higher temperature (above bp of reflux solution) acids can diffuse through CNTs wall and reach the catalysts, because mostly catalysts located in the inner layer of CNTs. As a conclusion, higher temperature cause the mobility of ions increase and mass transfer enhance. I also would like to refer you to my paper that published and is mostly about purification of MWCNTs. Below you can find the link on Science Direct.
http://www.sciencedirect.com/science/article/pii/S0169433211005101#
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