Well, there is an error in this "What if". it states:
This is wrong
The Huygens probe, which descended with batteries nearly drained (taking fascinating pictures as it fell), succumbed to the cold after only 26 seconds on the surface. It had enough time to send back a single photo after landing—the only one we have from the surface of a body beyond Mars.
I remember that the Huygens sent more than a hundred of pictures from the surface, the problem is that the camera was not steerable and it took allways the same picture. From the wikipedia we have the correct answer:
The main mission phase was a parachute descent through Titan's atmosphere. The batteries and all other resources were sized for a Huygens mission duration of 153 minutes, corresponding to a maximum descent time of 2.5 hours plus at least 3 additional minutes (and possibly a half hour or more) on Titan's surface. The probe's radio link was activated early in the descent phase, and the orbiter "listened" to the probe for the next 3 hours, including the descent phase, and the first thirty minutes after touchdown. Not long after the end of this three-hour communication window, Cassini's high-gain antenna (HGA) was turned away from Titan and towards Earth.
Very large radio telescopes on Earth were also listening to Huygens' 10-watt transmission using the technique of very long baseline interferometry and aperture synthesis mode. At 11:25 CET on January 14, the Robert C. Byrd Green Bank Telescope (GBT) in West Virginia detected the carrier signal from Huygens. The GBT continued to detect the carrier signal well after Cassini stopped listening to the incoming data stream. In addition to the GBT, eight of the ten telescopes of the continent-wide VLBA in North America, located at Pie Town and Los Alamos, New Mexico; Fort Davis, Texas; North Liberty, Iowa; Kitt Peak, Arizona; Brewster, Washington; Owens Valley, California; and Mauna Kea, Hawaii, also listened for the Huygens signal.
Source: Wikipedia: Huygens_(spacecraft)#Detailed_Huygens_activity_timeline
So this means (in bold) that the Huygens continued transmitting data from the surface of Titan for more than 30 minutes, actually I remember that it was something like over 2 hours but I did not find information about it now.
There is however an interplaneray spacecraft that succumbed 14 seconds after landing, but it was in Mars, The Mars 3 from the Soviet Union...