I was wondering if there was any way for a spy to stab a heavy who had the Huo-Long heater deployed without getting set on fire. The ring of fire seems to come out at intervals of flame no-flame, but every time I have tried as spy I've always ended up set on fire. So aside from the obvious "stab when he isn't shooting" is there any way around this weapon's effect?
To avoid getting burned by the Heavy's Huo Long Heater, instead of charging towards his back, try jumpstabbing from higher positions. Hold crouch while positioning yourself on top of him, then stab when you land on him (remember to hold Crouch).
Trying to run to his back and stabbing him will set you on fire, even whilst the Heavy dies. So for these guys, I typically try jumpstabbing.
If you care less about getting burned, and more about making kills, use any knife besides the Spycicle. The Spycicle will be consumed when hit with fire, rendering your one-hit kill backstab gone, so take care when choosing the proper knife for the job.
If you care more about your life than making picks, then go with the Spycicle. At the very most, if you attempt to bypass that half-second delay of flames from the Huolong, and mess up, you can still get away without getting burned.
One technique is to activate the Dead Ringer after a successful stab. You will be set on fire briefly (taking slight damage), but the Dead Ringer's effect will extinguish the flames.
It's very important that you activate the Dead Ringer after stabbing the Heavy (or at least after retreating if you feel your cover is blown) or you will be set on fire while cloaked. Not only does this reveal your location to enemies, the fire will also drain your cloak time, leaving you very vulnerable.
When dealing with Huo-Long Heavies, I use the Conniver's Kunai and the Dead Ringer. The health absorbed from the Heavy compensates for the damage caused from the fire ring and if you want to be cautious you can use the Dead Ringer. If you don't want to backstab, for some reason, I would recommend the Ambassador as its critical damage from headshots is helpful for quickly taking out the Heavy from long range.
(some advice with the Ambassador: before trying to use it, be sure that you can aim well using only the crosshair, and be sure you're far enough away to not attract the Heavy's attention. Also, use the Ambassador as a last-ditch option, as it is easier to just sneak up behind the Heavy and backstab him.)
EDIT: After further research, jumpstabbing as @Retrosaur mentions is probably the most direct way to deal with the Huo-long. It's effects are only along the ground!
The Spy-cicle will let you get in close although you can't necessarily stab them at that point. But it does regenerate pretty quickly, I use it with the ambassador, to do a sort of head-shot backstab on weaker targets or even foolish heavies.
The ammo drain of the Huo-Long means the heavy must be next to an ammo source to fire continuously, the weapon's only major weakness. Try to keep this in mind as you plan a take down for him, he's got to stop firing and run for the ammo if he's out in the open.
Often times I use a combination of the dead-ringer and the Spy-cicle to help me more properly fake a death. Once people are convinced of your death, they often times more vulnerable. I use the dead ringer in repeating strike runs, so that I'm always swooping in and out of melee range making it unclear whether if I'm truly dead or not.
Tip: The Ambassador is a reliable way to kill unprepared snipers, even good ones are usually suckers for it.