Plasma coolant was considered a biohazard and would react violently with organic matter, liquefying it on contact. The USS Enterprise-E's warp core had two plasma coolant tanks. (Star Trek: First Contact)
The loss of plasma coolant causing adverse effects to the warp core does not seem to apply to the USS Enterprise-E. In Star Trek: First Contact, when Data breached the primary coolant tank in main engineering, it did not appear to have any adverse affect on the engines, even though the warp core was powered. It is possible that Starfleet engineered a solution to this problem by having two tanks so that in the event of the failure of one, not all the coolant would be lost. It can also be hypothesized that since the warp engines were not active during the "First Contact incident", the rupture of one of the two visible plasma coolant tanks was not sufficient to cause a thermal overload of the warp core reaction chamber.