The Destiny 2 In the Hot Seat triumph is one of the many challenges that make up the revamped Solstice of Heroes event. You have to complete each of these in order to earn Kindling; a vital resource in upgrading your Candescent Armor (opens in new tab) so you get even better stat rolls, a guaranteed +20 in a stat of your choosing, and also restore the visual glow of the armor itself.
But some challenges are more straightforward than others. Just like the confusion around the Empty Grief (opens in new tab) or Nullifying Reconciliation (opens in new tab) challenges earlier in the Season of the Haunted, In the Hot Seat doesn't really provide a whole lot of detail in terms of how to progress said challenge. In this In the Hot Seat challenge guide, I'll explain how you can earn that Kindling and Event Ticket, and progress towards the Flamekeeper title.
Destiny 2 In the Hot Seat: How to complete the challenge
Now, you're probably wondering why you're making such slow progress with the In the Hot Seat challenge. Just like the Hand Lighter or Shotgun Solstice challenges that require you to kill stuff with those weapons, you have to do it a whole lot in order to complete them. This challenge is to "complete activities within the Throne World to earn Silver Leaves" and the Vow of the Disciple raid offers by far the most progress towards the triumph at 35%.
However, Vow takes a while and you might not have a raid team, in which case your best option is to complete the Wellspring activity. This grants you 10% progress per completion and also has a chance to drop red border craftable Throne World weapons which rotate daily. Since you have to craft a load of these as part of the investigations to earn the exotic glaive, you can kill two birds with one stone.
Lost Sectors also offer 5% progress while Public events offer 3% for regular, and 5% for heroic completions. Either way, you're going to be farming a lot of activities if you want the triumph.