Regarding heat buildup of the shield matrix system: further research/practice is needed to determine specifics, but it was my intuition that the additional heat buildup is low enough to be counteracted by about one or at most two units of coolant.
Practically speaking, even uncooled the time until overheat is long enough for medium-length engagements, and even if one unit of coolant is not technically enough to counteract all heat produced by the matrix, it should still vastly increase the time until overheat (which gives the engineer ample time to either redistribute coolant or inform the CO).
In short, engineers can likely assume practical heat stability with tho units of coolant in total (one for front shields, one for rear), leaving six units for other systems. Since benefits of additional energy that is fed into a system is non-linear and subject to diminishing returns, this should allow ships to still operate at about 75 – 90 % efficiency (compared to boosted baseline without shield matrix), broadly speaking.
It should also be noted that the matrix can be switched on intermittently for short amounts of time. This will still redistribute the charge of the shield capacitors, while being very light on heat generation. Ships can thus still aid each other in shield recharge with little impact to their own systems.
In combat, the mental load on comms officers and the sometimes rapid change in shield values makes this approach non-ideal for various reasons; on the other hand, if the battle group is regrouping (perhaps from different parts of the sector) and a number of vessels are at full shield while others are not, even just switching on the system for a second will allow a significant decrease in time spent recharging shields (depending on circumstances).
I disagree with some of the tactical implications Tetra mentioned:
I would argue that the biggest benefit of the shield matrix is when the entire battle group is toe-to-toe with the enemy, rather than having all ships but one stay outside beam distance. Since any incoming damage is distributed among all ships anyway, damage dealt to the enemy should be maximized by having all ships fire on the enemy.
Comparative to established focused fire, the damage the lead ship can take (and thus the staying power of the battle group as a whole) is at least multiplied by number of ships in the vicinity; if outgoing damage is reduced by having other ships stay away, this advantage is mostly negated.
On the contrary, the shield matrix can even be exploited by having the lead ship focus on damage mitigation, while the rest of the battlegroup focuses on dealing damage. This leaves each ship in a specific role in the engagement, and thus in a position to optimally use their coolant/energy.
Of course the above is assuming the enemy ships are focused on the lead TSN vessel, but tango can be established before engaging so this assumption should hold most of the time. And even if not, if the battlegroup stays close any enemies would be close enough to shoot at something anyway, so incoming total damage will be the same.
This also does not include ships specifically tasked with e.g. Kappa of course, but that is a situation where said ship would not contribute to damage anyway (by design).
An emergency situation (e.g. a tractored ship) is generally one in which “you miss every shot you don’t take” should apply. Thus, both the ship in danger and all others coming for help should make it a priority to also activate their shield matrices as soon as possible (for the latter, perhaps even before being in range). The case in which it is “too complex to get active in time” is the same as not trying at all, i.e. the worst case. So the attempt should always be made.
It will probably be beneficial to practice this so comms officers can act quickly if needed.
A special highlight in this regard is the “Lancer-loop:” even if an incoming ship overshoots and thus needs additional seconds to actually turn about and help (which is not ideal in the first place), an active shield matrix would still engage on first contact, so help the ship in danger immediately. Even if the ship gets out of range again a second later, shields will have averaged intermittently to buy additional time.
If that is not even attempted, there is less chance that the help will be in time to save the ship.