A large (8 metre) branch fell on my Thule box splitting the upper carcass in many directions (both seams and field areas), in addition to the complete break of a front lower segment. I decided to try and fix it despite finding a replacement. Well I have to say, it worked out great, and it did not involve expensive epoxy, adhesives, hot air welders, or any of the methods most commonly referred to. Thule's cargo boxes are made from ABS plastic. The same black plastic material used for your household domestic waste plumbing systems. Rather than use foreign (non-ABS) material as your binding agent, simply use ABS. By keeping the joint material native, you are essentially re-establishing the continuity of the original material.
Take a small piece of ABS pipe (any scrap will do, just ensure it's ABS -- will say on the side) and grind it down in shavings. I used a rotary cutting tool with a bit that looks like a common router bit for rabbit joinery. This resulted in very small shavings. Accumulate enough shavings and place in a small glass jam jar with a lid. I had to cover roughly 1.5 metres in crack length and found ABS shaving volume equal to a couple marsh mellows to be plenty. Here's the magic.... pour a small amount of Acetone into the jar and stir the contents (do it outside as it fumes) -- add more as needed just to get it to the consistency of carpenter's glue.
After you have bound the cracked segments of your Thule from the outside (I used rubberized packing tape as it has great horizontal field strength but can be removed easily). The tape up job doesn't have to be pretty, just ensure the edges are tight together and the tape is firmly holding it tight. On the inside, use a rotary cutting tool and any cutting bit to grind a trough directly where the cracks are. I went down approximately 3 millimetres and across approximately 8 mills. I left it rough to the touch. Clean the trough with Isopropyl alcohol; let dry.
Using a small paint brush (ones you find in elementary school water colour paint kits are fine) "paint" the trough with the dissolved ABS from your jar. The advantage here is the Acetone in the mixture dissolves the edge of your trough so both the slurry (your mixture) and the hard carcass body are naturally bonding. As you might imagine, the Acetone will evaporate leaving nothing behind but ABS -- as hard as the original, fully bonded to the original material. Once dried, apply additional coats to build up the trough to your preferred profile.
Remove the tape on the outside and you're set. You could apply some sealant to the outer surface of the cracked area, but I did not as keeping it clean to look at on the outside is difficult when adding to the perfectly smooth outer surface.