I checked the manual of the LD and Temperature Controller - CLD1015 
It is possible to modulate the current with an external source.
The input is a SMA connector on the rear panel of the controller.
Details on the modulation parameters are in the attached table (from the manual)

manual link: https://www.thorlabs.com/drawings/a2689db57be706ee-B083F81C-0501-84ED-9463F9E7DF4E37B5/CLD1015-Manual.pdf