Rd = detection range (km)
A = spacecraft projected area (m2 )
T = surface temperature (Kelvin, room temperature is about 285-290 K)
If the ship is a convex shape, its projected area will be roughly one quarter of its surface area.
A Russian Oscar submarine is a cylinder 154 meters long and has a beam of 18 meters, which would be a good ballpark estimate of the size of an interplanetary warship. If it was nose on to you the surface area would be 250 square meters. If it was broadside the surface area would be approximately 2770. So on average the projected area would be 1510 square meters ([250 + 2770] / 2).
If the Oscar's crew was shivering at the freezing point, the maximum detection range of the frigid submarine would be 13.4 * sqrt(1510) * 2732 = 38,800,000 kilometers, about one hundred times the distance between the Earth and the Moon, or about 129 light-seconds. If the crew had a more comfortable room temperature, the Oscar could be seen from even farther away.