It usually depends on how good the reference card is in terms of PCB layout and heatsink/cooling. If it's a great reference cooler and PCB, the card is unlikely to be modified by 3rd parties as it costs them money to do so. However, later on, 3rd parties often introduce new cooling solutions (e.g. single slot, passive) to differentiate their product more often than not and hopefully sell some additional units, though it depends on which card and whether there is a market for it.
For instance, I bought a passive Radeon 4350, which didn't exist at launch, but was quickly made as it became clear they were a great option for a HTPC, which needs to be quiet. Passive 8800GT cards for example didn't emerge for a long time after.
Actual times and numbers will just take some hard research, I don't think anyone has done this for you already, so have fun finding out what you need! Don't forget review websites are a good resource for additional information and insight over what the manufacturers claim.