When you click "Intercept", the intercept vessel list gives you ETA to given destination. Day and Night last approximately 12 hours each (changing with latitude and season) so you can estimate when to launch your craft so that it reaches the destination after dawn and before dusk.
For example, you have downed an UFO in India. The "Intercept" screen gives ETA of 8 hours for Shrike-1 to reach the site. That means you should wait until the crash site is past half-way between the dusk and dawn terminator lines.
If the UFO was freshly downed, you can just "patrol" until morning. But if the UFO lay there for a while, or it's a terror site (these don't last as long) it may vanish before the right time to depart arrives. In this case you may utilize a small "exploit": neither a downed UFO nor a terror site will vanish if the landing craft is en route. In this case exploit the excessive fuel capacity of your craft. First, save to determine the moment the craft/site vanishes. Then load the save and send the craft ahead of time in the opposite direction, to any random location in the world opposite as the UFO. Target it before it vanishes, and due to the route being longer, you will arrive after dawn.
Also remember you can redirect a returning dropship and handle several sites in one go. Dead and wounded soldiers will still be dead or wounded, but all ammo and equipment is resupplied, and the tanks regenerate all health (providing they weren't destroyed). That way you can handle a distant group of downed UFOs in one day.