This proof of concept is about communicating from a non-air gaped machine to an air-gaped (not on the network) machine. Both machines need to be infected with the malware. This would be like a stuxnet type of attack; it may be possible to get one time access to the air-gaped machine to install the malware, but you can't get continued access because you need to physically leave the air gap.
The way the communication works is by modulating heat on one machine and have the other machine pick up the change in ambient heat. It requires the two machines to be physically close. It may be possible to expand this to a greater range, but perhaps a more likely scenario is where you have networked controlled HVAC and temperature sensors all over the room which are also networked and which you can monitor. In this proof of concept, it posits that all of the servers are nearby, but some are airgaped; an organization may just not connect systems to a network, but not bother to put them in another room.This is more of a nation-state spying type thing then something a script kiddie or even criminal hacker would be up to.
The difference with other attacks where you remotely view the changes in power, etc is that the air-gaped computer is more likely to have temperature sensors to read input and also can control the fan, processors, etc to control heat. This means that the air-gaped machine does not require any additional hardware once compromised with malware to transmit messages back to the non-air-gaped machine. Also, because it takes a good amount of time to change temperatures and ensure its consistent, the communication is slower.
Again, this is a proof of concept. Check out the wired article, geeks.com is probably not the best place for deep technical reviews.
There are similar classes of "remote viewing" attacks with reading power levels, radar, etc.