A home made copper 'radiator' is ok to use IF it doesn't move. I have put 1,500-PSI through small diameter copper on nitrogen tanks with great success. You can flare it or use IFF (inverted flare fittings). I prefer to flare 3/8" copper. Along with great heat transfer and wonderful flexibility, another reason I like copper is that I can solder it or solder copper wires to it. Steel also solders well to copper if you get the heat up there (great for a rock shield).
Air conditioning guys coil copper between vibrating parts but hoses work as well. Make sure your hose is made for oil and certified for 100 PSI. Long (or coiled) steel lines vibrate well without breaking, like your transmission lines. - Dave