Thanks Kirk good suggestion.@KirkKuykendall gave a good suggestion of:
Have you considered launching arcmap from a bat file that sets the LocalAppData variable before running arcmap.exe? http://environmentvariables.org/LocalAppData https://stackoverflow.com/a/3036367/125400
but I've found that this can be done from the registry as well.
toTo quote the ESRI technical documentation:
The Cache Path can be changed by setting a new string value “Cache Path” at HKCU\Software\ESRI\Desktop10.x\Settings. If the settings key does not exist, it can be added. This key and string value can be created or viewed by opening ArcMap and navigating to Customize > ArcMap Options > Display Cache.