Flame Whip + Holy Light

If Flame Whip touches Sun Armor, it becomes Holy and gets affected by Buy the Holy Light

Starting sustainability against 1.0.7c burst meta is achieved by instant Glowing Crown (if you have Prismatic Orbs), Stone Helm or Cap of Discomfort (which is also super good agaist buffs scaling builds). 
Repeater is always good to play here: because of heat scaling, it's cooldown lowers and it repeats caps' damage reduction almost immediately after the starting reduction ends. 

Heart Container or Heart of Darkness with their +100 max HP are also good sustainability. Heart of Darkness < Cap of Discomfort and it is only worth crafting if you have a lot of Corrupted Crystals and starting Regen. Please note that Heart of Darkness is not affected by Buy the Holy Light.  

Sun Armor, Shelly and Turbo-Shelly are nice options to heal, because heat lowers their cooldowns.

Djinn Lamp > Pineapple in the speed of gainig spikes, it is also fast trigger if you play with Goobert. +27Damage gain is possible if you have Flute or Gloves of Power. Oil Lamps are great for damage scaling.

Speaking about stamina, 1 Wolpertinger usually would be enough to solve stamina issues, if you play Flame Whip as the only weapon. Sometimes it might run out of Stamina, but you'll be able to print Heat non-stop. 
If you also play Burning Blade, make sure to have Everburning and more Wolpertingers. Heroic Potions and Amulet of Alchemy might be worth if you have many Stamina Sacks.
Shields with Shielded may cause problems anyways.