Question: Are there situations in which a pilot could/has to lower the landing gear during flight for reasons not directly connected to landing? (i.e., not part of the landing checklist)

Originally I thought I had seen some around the location indicated by the pin on the map below (17° 25' 30.093" N, 78° 32' 27.4734" E), in the evening time around 4:00 and the weather was clear.

[![Sighting location](https://i.stack.imgur.com/78nOO.jpg)](https://i.stack.imgur.com/78nOO.jpg)

Answer: 
I am on a U.S. Air flight right now. Pretty sure that the plane is an A330. About 20 minutes after take-off, the pilot said that he had to lower the landing gear to cool off the brakes. After about 3 minutes of much noise, and some chop, he raised them and said that it had worked.
Sure it's a private ***jet***? Plenty of single-engine piston powered aircraft have fixed landing gear.

Most jets cruise at high altitudes, so if you can a) see the aircraft, b) identify it as non-commercial, c) notice the landing gear is down, and d) claim that it's not near an airfield then it's more likely that it is a 4-6 seat piston single with fixed gear. Cessna, Piper, Beechcraft have made thousands.

Addendum to edited question:
You say there are no airports *near by*. Possible there's one a little further away? Planes typically raise the gear as soon as they are off the runway, but they lower it 30km out. And that's 30km flying distance, not driving diatance.