For something the size of a plausible ship, the surface area is astronomically smaller, while the temperature of most of its surface would likely be kept at or lower than the range which is compatible with macro-scale organisms and biochemical processes. A ship would also be trying to manage its heat, probably using an insulating exterior.
Meanwhile it would be pointing its thruster - the only part meaningfully above 300K - away from you for at least half the trip if directly oncoming, with angular efficiency coefficients if heading somewhere else. Recall that the ship itself is insulated & temperature-regulated, and therefore shields the emissions of the thruster. The thruster would also likely be focused as much as possible, so we could expect thermal radiation at steeper angles to drop off sharply.
Even something like a nuclear pulse rocket would be hard to spot until it was within a very small neighborhood, and then it would be up to whether you're actually observing that part of the sky during the time when it might be visible.
Ships are very hard to detect until they're almost on top of you.