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This is the first time I'll be using a heat-sink on a transistor. Right now these are just placed together.
Is the mounting correct?
TO-3 devices are typically mounted on the inside of any enclosing heat sink, rather than the outside. The way you have mounted it would prevent the part from being soldered directly onto a PCB.
Also, there are TO-3 specific heat sinks available, many of which would take less PCB real estate and typically provide better cooling than the one you have used. Heat sink selection involves required space, material (copper / aluminium / other), shape (flat / enclosing / raised), fin type, and expected thermal wattage to be cooled, as parameters.
Wrap-around design heat sinks also shield nearby components from the heat generated by your device, an added benefit.
The mounting that you show in your picture may be appropriate for your application. That mounting does imply that you are using a wiring harness to connect to the TO-3 leads. If the device was meant to solder into a circuit board of some sort, particularly if there were multiple devices side by side, you would place the TO-3 package inside the fin area and let the leads stick through to where the heatsink assembly can be placed down onto the circuit board.
Do note that the devices in packages like the TO-3 are getting rather uncommon in new designs. The large size of the device package makes product packaging very large. When you look at the types of packages used for modern day high power designs you will see characteristics that allow for higher speed operation, smaller product case sizes, more efficient device to heatsink coupling, and fewer piece parts on the BOM (bill of materials).
The advantage of the TO-3 case is <1.6'C/Watt thermal resistance vs the TO-220 of <1.8'C/Watt. No heat sink gives you 50 to 70'C/Watt junction to ambient thermal resistance. Considering your heatsink may only increase the "effective" surface area of the TO-3 by eyeball, a factor of 4, I would estimate your thermal resistance is around 12'C/Watt. Now considering you got this really big low thermal impedance transistor, does it make sense to mount it on a really "high" resistance small chunk of extruded aluminum metal.
It would be like using jumper cables to drive 10 Watt speakers. So yes I would say there is something wrong with this picture. Either you underestimated the temperature rise of this 15 amp transistor or you just happen to prefer bulky parts over the TO-220 plastic cases with metal tabs and are hoping for the best.
You would be better off with a TO-220 and larger thermal mass and surface area. The electrical insulator is necessary next to the transistor to prevent shorts since you can't really enclose a "live" heatsink as that insulates it ... read "increases the case-air thermal resistance. Also the surface needs to be large enough to ensure it is also very flat as any air gap insulates the part or adds 'C/Watt like Ohms Law for temperature rise.
For tips on cooling look at some CPU heatsinks for 100Watts both passive and force air cooling and compare your requirements.
You can often get old ones free or cheap surplus from PC shops. You can learn a lot by studying other designs. There are also TO-247 NPN power transistors with insulated mounting holes. But these "big old" silicon transistors are work-horse silicon power devices as active load devices and series bypass regulators, just don't try to push it to 200'C max spec and expect it to last too long. If it gets too hot to touch, you might want to lower the thermal resistance or share the load.