Long Range
Using long range weapons only, the Jupiter 3 does not overheat. 12 from HAGs, 12 from UACs = 24 + 2 movement - 4 "free is less than the 12(24) heat sinks it carries.
two HAG/30 = (2.4 + 2.4) *.75 (low ammo) = 3.6. So the FLK at long range is 4 (round normal).
Add in the two UAC10s at 1.5 each, and you have 6.6, or round up to 7 base long range damage.
Unfortunately, at medium range, those ER MLs hurt it more than they help. They push the heat up to 36 (12 from HAGs, 12 from UACs, 10 from ERMLs, 2 from movement).
6.6 + 1 = 7.6, or what would be an 8. But 7.6 * 24 heat dissipation / 36 -4 "free" = exactly 6. So it only gets 6 at medium range, but OV2 from dropping from 8 to 6 due to heat.
The FLK is also reduced due to heat, 3.6 * 24 / 32 = 2.7, or a 3 at medium for FLK.
The increased damage for HAGs at short range then bump the short back up to 7 again and 4 for FLK at short.