New main objective: Heat the Convector
Press TAB, open Magic, head to Destruction and choose Arniel's Convection from the list (screen above).
Stand in front of the Convector and in accordance with the instruction received from Arniel, hold down the mouse button for at least three second (screen above) to heat up the Convector.
New main objective: Retrieve the soul gem
Afterwards approach the Convector, interact with it again and take the Warped Soul Gem (screen above). All the above actions have to be repeated two more times with the Dwemer Convectors you choose.
New main objective: Deliver the soul gem to Arniel
You will be able to return to the quest giver only after finding three Convectors and heating up the Gem in each of them. Head to the College of Winterhold and give the Warped Soul Gem to Arniel (screen above). Sadly, you won't receive any prize this time as well.
New main objective: Talk to Enthir
With the fourth quest, you will probably have to wait around two days. You might have problems with finding Arniel. He's most probably inside a small storage room at the Hall of Countenance (screen above). Speak to him and ask if he needs any more help. The mage will share good news about the progress that he has made and will send you to Enthir, who for inexplicable reasons doesn't want to give you an item needed for his work.
As a reminder, Enthir can be found inside one of the rooms of the Hall of Attainment. Speak to him and mention the second item that Arniel is demanding (screen above). Enthir will insist that it's not his fault and the courier didn't get to him. You can of course ask him about the last known location of the courier, as your mission will be to locate him.
New main objective: Find the courier
Open the world map. You will have to search for the courier and the item for Arniel in a randomly chosen location. Find it on the map and plan your journey. After reaching the destination, you will have to explore some ruins, a keep or other construction occupied by monsters or living enemies (screen above).
Regardless of whether you started the search at once or postponed it, you will find the courier dead. Search for his body, probably found in a well guarded place (screen above). Examine his body and take the Keening.
New main objective: Deliver the package to Arniel
Return to the College of Winterhold and head to Arniel with the found dagger, without having to speak to Enthir. Arniel will probably be inside a small storage room at the Hall of Countenance. Approach the mage and give him the dagger (screen above).
New main objective: Observe Arniel's experiment
Now you will just need to watch the experiment that Arniel has been preparing (screen above). The whole process will surprisingly end with the disappearance of the mage. Note that you were rewarded with the Summon Arniel's Shade spell, thanks to which you will be able to call in the mage for help at any moment. Apart from that you can also pick up the Keening which luckily didn't disappear together with Arniel.