For clans... you don't get a choice so nothing for me to get mathy on.
For simplicity I will be using the following abreviations
SHS=single heat sink
SHSQ=single heat sink cooling
SHSC= single heat sink capacity
DHS=Double heat sink
DHSQ= Double heat sink cooling
DHSC= Double heat sink capacity
IHS= internal or engine heat sink (the base 10 or less heat sinks built into the engine)
XHS=external heatsinks
BC=number of bonus heat sink slots in the engine
These calculations assume a base engine heat capacity of 60
SHSQ= IHS*0.11+XHS*0.12
SHSC=60+IHS*1.2+XHS*1.2
DHSQ=IHS*0.2+XHS*0.14
DHSC=60+IHS*2+XHS*1.4
Ok so it's obvious (to me anyways) that the only potential use case for SHS over DHS is where you're critical limited and run hot. This means the only real potential beneficiaries are going to be energy boats of the heavy and assault classes.
This of course assumes that all critical slots are equal, but DHS cannot fit into the legs. As a result, the practical limitation on XHS for DHS is 9-12 XHS depending on loadout.
For illustrative purposes let's use the stock awesome 8Q loadout of 3PPC and 1SL and compare DHS and SHS.
With a STD engine the 8Q can fit 10 XHS if it uses DHS yielding DHSQ=3.4
For comparison you need 19 SHS to roughly equal that amount of cooling.
Now, with the awesome you can upgrade to a STD300 to get 2 BC and have tonnage to fit another 2 DHS yielding 12 total. Giving you DHSQ=3.68 and DHSC=96.8
One could also, if one is content to be long range energy support, use SHS, use endo,keep the stock STD240, add 24 XHS and get a SHSQ of 3.96 and SHSC=100.8
Ok, analysis time.
With SHS you get about 7.6% better cooling and 4% better capacity in our awesome test case. At the expense of about 10kph AKA moving at dire whale speeds.
So, it seems to me that SHS need another buff or DHS need another nerf for SHS to have a more common role in mwo. Personally I'd suggest making engine heat sinks not be true DHS. Now before you shoot me let's look at the effect in our Awesome test case.
Before our awesome had DSHQ=3.68 and DHSC=96.8. By making the IHS no longeer be true dubs we would see a 0.6 reduction in cooling rate and decrease in capacity of 6.
In our edge case that'd give the SHS awesome 30% more cooling and 11% more heat capacity.
That is a difference that is potentially worth trading about 1/6 of your possible speed for and is the kind of hard trade we should be looking at forcing pilots to make when they select between SHS and DHS. Naturally, DHS would still overwhelming be favored in most situations, but there'd be enough edge cases where SHS are worth the trade in speed and armor that people might actually use them
Thanks for taking the time to slog through all this and if you find any errors or have any comments (or job offers

TL:DR SHS are better but not worth it outside of a few highly improbable edge cases