its worth looking at the Sale of Goods act, under English legislation ( Scotland is different being 5 years) a consumer has 6 years to report a defect inherent at the time of manufacture to the seller ( not the manufacturer) , it doesn't mean goods should last 6 years but if its reasonable to assume that a faulty rad was caused by as manufacturing defect ( more than likely it was there if other bikes last much longer) then you may have a claim with your dealer. There are cases where items are portrayed or described as being suitable for a purpose these be included or where its reasonable to assume an time should last a specific time.
Ducati offer a warranty of 2 years
in addition to your statutory rights , reason its 2 years is to comply with an EU directive on consumer goods but your contract lies with the supplying dealer and their sale of goods contract lies with the manufacturer.
The DTI provide a guide for traders in
pdf format which is a useful guide to understand your rights and what remedies they can offer.