The fans wouldn't run faster. The memory would run hotter, but the total heat output remains the same. The inadequate heatsink just needs to reach a higher temperature to conduct the same amount of heat from its smaller surface area.
If anything, the fans would run slower initially, as it would take longer for the memory to reach a point where it effectively radiates the same amount of heat.
The only manufacturing change that needs to happen for already ramping FB-DIMM production lines is to make an extrusion tooling to produce the desired profile of aluminum heatsink.
Supply will match demand in a few weeks. Prices will remain high for a few weeks after that, but in 2-3 months the market will adapt, and FB-DIMMS will drop to a price that's comparable to other server-grade memory.