Does anyone know the calculation for the current base temperature of a system body?
I suspect it's a simple matter of star brightness and current distance from star.

Prior to eccentric orbits, the base temperature of a body never varied, so I could just use the value of FCT_SystemBody.BaseTemperature.
But that value seems not to vary over time.

I'm good for this question; I had to derive it to match Aurora's model to get my body planner to work the way I wanted it to. It largely follows Pedroig's link and can be simplified even further for the values we have access to:

BaseTemp (K) = SysConst * L^0.25 / AU^0.5

L is the star's brightness measured in solar units; AU is the body's current distance in AU (works with eccentric orbits as a result). The system constant I didn't bother to break down further; it's value appears to be exactly 255 for all systems other than real Sol when plotted. Real Sol uses something between 255.13 and 255.3406815 (I've been too lazy to nail it down precisely) to determine base temperature. Rotation rate, atmosphere, and albedo are all modeled during the surface temperature calculation while the Stefan-Boltzmann constant is baked into the ~255 system constant.

Because the terraforming tab still uses 255 for its math even in Sol, bodies in Sol are slightly warmer than their listed terraformed values. This is most evident with the maximum periapsis temperature when they're located at periapsis. Venus was the first that I caught doing this as its temperature is the highest and least susceptible to hiding the error in rounding; see attached screenshot.

I'm scratching my head as to why my Jump Stabilisation Ship is tracted at a meager 342 km/s. Is there a penalty at some point if the masses of the two ships are vastly different? 
My Tug is 10,000 tons and has a speed of 2400 km/s. My Bïfrost JSS has a base speed of 333 km/s. So what gives? 

There are two important rules here:

• A ship under tow does not contribute its own engine power to the speed of the fleet.
• The speed of a tug plus a ship under tow is determined by the tug's engine power and the total mass of both the tug and the towed ship.

Given this, you have a total of 480 engine power on the tug, and a total of 70,000 tons (tug 10,000 + station 60,000) or 1,400 HS. 480 EP / 1,400 HS * 1,000 = 342 km/s, so the numbers check out correctly.

I'm scratching my head as to why my Jump Stabilisation Ship is tracted at a meager 342 km/s. Is there a penalty at some point if the masses of the two ships are vastly different? 
My Tug is 10,000 tons and has a speed of 2400 km/s. My Bïfrost JSS has a base speed of 333 km/s. So what gives? 

TG-01 Sheperd 001  (Sheperd class Tug)      10 000 tons       114 Crew       360.5 BP       TCS 200    TH 480    EM 0
2400 km/s      Armour 1-41       Shields 0-0       HTK 47      Sensors 5/0/0/0      DCR 1-1      PPV 0
MSP 132    Max Repair 100 MSP
Tractor Beam     
Lieutenant Commander    Control Rating 1   BRG   
Intended Deployment Time: 3 months   
● Recreation Room-25    ● Library-25    2x ● Escape Pod-5    ● Security hardpoint-5   

Honeywell Aero Nuclear Thermal Engine C80 (6)    Power 480    Fuel Use 10.06%    Signature 80    Explosion 5%
Fuel Capacity 850 000 Litres    Range 152.1 billion km (733 days at full power)
Refuelling Capability: 50 000 litres per hour     Complete Refuel 17 hours

Silas-Nein Small Thermal Sensor 1-5 (1)     Sensitivity 5     Detect Sig Strength 1000:  17.7m km

This design is classed as a Commercial Vessel for maintenance purposes
This design is classed as a Tug for auto-assignment purposes

JSS-01 Bifröst 001  (Bifröst class Jump Stabilisation Station)      60 000 tons       197 Crew       1 384.8 BP       TCS 1 200    TH 400    EM 0
333 km/s      Armour 1-136       Shields 0-0       HTK 52      Sensors 5/0/0/0      DCR 1-0      PPV 0
MSP 24    Max Repair 1 000 MSP
Commander    Control Rating 2   BRG   AUX   
Intended Deployment Time: 3 months   
Jump Point Stabilisation: 180 days
● Large Crew Lounge-100    ● Onboard Hospital-50    ● Recreation Room-25    2x ● Security hardpoint-5    9x ● Escape Pod-5    3x ● Medium Hydroponics-50    ● Promenade-50    ● Fitness Center-50    ● Library-25    ● Small Armory-5   

Honeywell Aero Nuclear Thermal Engine C80 (5)    Power 400    Fuel Use 10.06%    Signature 80    Explosion 5%
Fuel Capacity 1 400 000 Litres    Range 41.7 billion km (1449 days at full power)
Refuelling Capability: 50 000 litres per hour     Complete Refuel 28 hours

Silas-Nein Small Thermal Sensor 1-5 (1)     Sensitivity 5     Detect Sig Strength 1000:  17.7m km

This design is classed as a Commercial Vessel for maintenance purposes
This design is classed as a Stabilisation Ship for auto-assignment purposes


Does anyone know the calculation for the current base temperature of a system body?
I suspect it's a simple matter of star brightness and current distance from star.

Prior to eccentric orbits, the base temperature of a body never varied, so I could just use the value of FCT_SystemBody.BaseTemperature.
But that value seems not to vary over time.

Have to ask, there are Troops actually aboard said ship?

Asking from experience...

Yes yes there were troops aboard 

I figured out the issue, I had to create a colony before, Jesus Christ.