There are a couple of members with long experience of the Quad G5, such as ClassicHasClass and Applefreak. I have no doubt that both will respond once having read your post, but I seem to recall in an exchange with CHC myself that his Quad operates at significantly lower temperatures. 10º in the G5 CPU makes all the difference as far as fan speed is concerned.
I suspect that individual processors have different heat characteristics, and that this has to be factored into talk about what machine gets how hot, alongside of things like heatsink compound and dust. That one G5 does x does not means than another identical unit will do x as well, even when properly tweaked. I had, for instance, a dual 1.8 that ran much cooler than a dual 2.0, and I have a dual 2.3 (early 2005) that runs cooler than the 2.0 and is comparable to the 1.8. The 2.0 is the noisiest of the lot, and though for the most part it is a quiet machine for what I do on it (mostly office stuff), the fans do kick in big-time if the temperatures get up into the high 60s. Invariably, this happens on the web, and Flash is certainly a factor there.
Thermal tolerances are seemingly set/ tweaked by thermal calibration in software, and these can be checked in Temperature Monitor, which was already mentioned. The upper limit for my G5s tends to be high 70s or thereabouts (slightly different for the different machines, BTW), so if your machine is getting up there, it does need the cooling action of the fans, else damage will result.
Whether Flash "ought" to be causing these behaviours is something that others will no doubt weigh in on in due course, but we all know the Flash is crappy software that strains older hardware to the limit, and we had that confirmed by Apple's abandoning it for the likes of the ARM chip. It would be interesting to try HTML5 on the same site and see the difference.
The liquid cooling, of course, is a complicating factor in your case (are the pumps working, is there leakage, is the level adequate and is the coolant contaminated), but in my experience, the simpler resort of doing a thermal calibration can help a great deal with the fans. It was certainly so with a dual 1.8Ghz machine that I used for a while. It may be that yours is also one of those cases. You'd need to locate the appropriate "Apple Service Diagnostics" disk image "out there" to do the business, of course, and you would need the version for your machine or era specifically, but if I were you, and dust etc. had definitely been excluded as cause of this effect, I would try recalibration next. It can't do the machine harm (it is working now on the basis of the same process done in the factory) and it might do it a lot of good. Takes about 90 mins, during which the fans will run full blast, so plan to go out.... Essentially, if the physical characteristics of the cooling system have changed due to ageing, it would follow that the software controlling that system could likely use better information about those changed characteristics.