If you use kerosene or petrol make sure to flush/rinse it with fresh clean ATF in the end to remove any remaining cleaning solvent from the cooler.
When using petrol etc, its pumped backwards with help of air compressor and the effluent caught in a small pan or bottle so you can see the contamination coming out - its clean when the cleaning liquid coming out is clean. - Then do the final rinse with ATF (any atf) with help of air compressor.
In Karachi an aerosol can of oil heat exchanger was sold in some shops in plaza market - it was french or US origin I think and was pretty large, it was enough to clean the ATF cooler in one shot and it really really cleaned out the debris.