But a lot of that extra surface is aimed back at the spaceship.
Let's see if I can dig up some of my thermal systems knowledge from the dusty and possibly-haunted corner of my brain...
A Union-class Dropship has a height of 78m and a diameter of 81.5m. Being a bit conservative (and a lot lazy), I'll approximate the apparent cross-sectional surface area as seen from the side of the Union as a circle with the larger 81.5m diameter
From droplets X meters away from the Union's hull, the "seen" angle theta is the tangent of the apparent cross-sectional radius divided by the X distance from the hull (basically opposite/adjacent), so theta=arctan(40.75m/Xm). If the droplet is just 40.75m away, theta is 45 degrees, and the droplet basically "sees" a 45 degree cone from the center of the Dropship's cross section. At worst case scenarios (X is nearly zero), the droplet would "see" a nearly 90 degree cone (basically a semi-circle).
With a reasonable assumption that the droplet transmits equally in all directions, this is equivalent to a spherical emission. The "seen" hull is equivalent to a spherical cap cutting into that spherical emission; dividing the "lost" surface area from this spherical cap by the full surface area of the sphere should result in a rudimentary estimate of the % energy returning back to the Union, and 1 - that % = the approximate efficiency of this system.
Total Spherical area: 4*pi*r^2
Spherical Cap area: (1-cos(theta))2*pi*r^2
Spherical Cap area / Total Spherical area = (1-cos(theta))2*pi*r^2/(4*pi*r^2)
||
V
(1-cos(theta))/2
(Note: r^2 = UnionRadius^2+X^2=(40.75m)^2+x^2, but since it cancels out here this doesn't matter in this case)
In its worst case scenario (Droplet right next to the hull, theta ~= 90deg ) about 50% of the energy returns to the Dropship. Somewhat further away at 40.75m (theta = 45deg, which is still pretty close in terms of the vastness of space tbh) this drops to 14.6% energy return (or 85.4% energy jettisoned away). Placing the droplets further from the Union dropship will increase efficiency even further, albeit with diminishing returns.
IIRC that is actually pretty high without having to pump the droplets too far away. For Battletech's level of technological development, it seems feasible.
Note 1: Even though in this test case 14.6% is returning to the Dropship in this example case, that probably doesn't matter in practice. Unless the Dropship's exterior hull plating is made out of a black body material, not all of that 14.6% returning energy will actually be absorbed; some will be reflected.
Note 2: The energy that is absorbed is being absorbed by a relatively massive area of the Union's exposed hull, which will also tend to eventually re-radiate the energy as thermal radiation (albeit much more slowly per unit area than the superheated droplets since it's "colder"). While that amount of energy stored in a droplet stream can melt Battletech (or real life) plating when concentrated onto a small point like with laser weapons, when not concentrated the energy intensity would be more akin to a glorified flashlight. It's mostly important to get the waste heat out of your guns and lasers so they don't melt, if a bit of energy is redirected onto the ship's hull and raises it by a degree or two that's still considered a success.
Also the need to concentrate any heat to create the molten metal droplets will be far less energy efficient than the normal cooling system.
BT's normal heat sink systems also involve concentrating heat into material, the difference is that the canonical heat sinks pump it into fluid coolant which goes to a radiator system (SHS using heavy but space-efficient graphite radiators and DHS using lighter but space-intensive polymer radiators), while this version pumps it into molten droplet medium to be temporarily ejected out the ship. It pretty much has to be since radiation is so inefficient at low temperatures (radiation emission power scales with T^4).
The problem is, exposed to the vacumn space does not let those debris to reduce its heat. Only the radiation works on the space since there is almost no medium to transfer the heat, but for this you don't need to throw away those little debris in the first place and you could do better such as shoot the lasers instead. Add the big heat sink plate on the surface would serves the similar purpose too.
Also it surely pollute the course with those little debris, and although a few of those won't cause much effect but the constant and frequent uses of this may cause catastrophical result.
No, tiny droplets are one of if not the most efficient (in terms of per unit mass) method to increase heat dissipation via increasing surface area.
And the microparticle droplets would be of negligible concern in the vastness of space. Even if/when small amounts of material escapes the cooling system, the droplets will cool down extremely quickly, so getting hit by these superheated particles is not a major issue, and in Battletech there's already plenty of matter flying around in a fight from matter coming out through the spaceship exhaust, weapons fire, spaceship debris, etc. Probably far less practical in an atmosphere though, since you'll likely accidentally collect material from the atmosphere into your radiation system which is no bueno.
To the contrary... I think it´s a viable system. Radiating heat only happens on the surface, naturally enough, and lots and lots of tiny droplets have more surface per mass than larger objects of the same combined mass.
The main limitation I see that this would only work as designed in a vacuum and zero-g environment, not in an atmosphere, let alone while landed.
That's basically my take on this as well.
To OP: If you're interested in more hard sci-fi technology, I'd take a look at Terra Invicta for some inspiration. The technologies are more on the hard sci-fi side with a handful exception (Exotics being the magical alien material that helps some of the plotlines to work and gives them a technological advantage throughout the game), so it could give some ideas of potential technologies rooted in reality. The game itself is hard and time consuming, but pretty fun if you can get the hang of it.
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, I mostly play alpha strike. I've found that I like bigger games (400 points), but I don't like running too many new mechs at once because it bogs things down. So, I'll probably make a lance out of the new units and then try to rotate through all the new stuff over the rest of the year. I've never gotten this many at the once, so we'll see how it goes. 
