Correct me if I'm wrong, but I don't believe power out is meant for continuous usage (unspooling) as it can overheat the winch (and possibly melt synth line).
I've been learning a lot about winches recently.
If you're winch has an in the drum cone brake, as most do, that add heat to the drum when running the winch under power, and especially when braking.
That puts synthetic rope at risk of heat damage, as you pointed out. One solution is to use "fire line" or "fire rope" or whatever that's called. It's sold at winchline.com under one brand name, and at other places under other names. It's very heat resistant, though the guys who sell it told me that even that stuff can overheat and get damaged if the winch overheats enough.
T-Max does have an in the drum brake, but it's some type of drum brake (think car drum brakes, I think) that makes less heat than a cone brake in the drum.
The Superwinch LP8500 that I'm becoming fond of, has some type of in the drum brake that makes less heat than a cone brake. I don't know any more details about than that - because that's all that SW told me about it. I suspect it's some type of drum brake like T-Max uses. Makes less heat than a cone brake.
I'm not sure, but I think the Smittybuilt winches might also have an in the drum drum brake that's not a cone brake. I think Smittybuilt winches are made by the same outfit that makes T-Max, but in different pull ratings so as not to compete with each other).
The Superwinch LP8500 and all TMax (and perhaps Smittybuilt) models are more suitable for use with rope due to less drum heating. Even so, I'd use fire rope with those. I think they'd heat to much for regular syn rope, but fire line would handle it just fine.
This is where the Superwinch EP and EPi winches really shine. Their external brake system does not heat the drum, and it helps them draw less amps because no brake drag. Also, their motors, gearboxes, and solenoids are superior too. So they are the best for synthetic rope. On the downside, they are very heavy winches, even with synthetic rope. All other brands of 9K winch are much lighter install weight.
The Warn XD9000, Tmax 9K and 10K, Smittybuilt 8K, and Superwinch LP8500 are the lightest of the 8K to 9K winches that I know of, and of those, the Tmax and Superwinch LP8500 are the most synthetic rope friendly due to less drum heating than the Warn. I'm not sure about the Smittybuilt for drum heating, but I think it's probably same as Tmax (good).
Tmax would be awesome if they fix their hinky remote to operate safely. i.e. - stop winching immediately when you tell it to. Currently it continues winching after you tell it to stop, according to reviewers. That would scare the stuff out of me.
Anyway, your winchrope and drum overheating issues are less of a concern with Tmax all models, Superwinch LP8500, and possilbly Smittybuilt - because they have more efficient in the drum brakes that make less heat (and allow less amp draw).
The very best for a cool drum is the Superwinch EP winches because they have an external disk brake that adds not heat to the drum, and allows even lower amp draws than the LP8500. Also the EP winches rock for line speed. I just don't like how much they weigh. Their install weights are very heavy. Even with rope they're still heavy.
A Superwinch EP9 with rope
weighs about the same as an SW LP8500, Tmax 9000, Smittybuilt 8000, or Warn XD9000 with cable.
Yipes! Now, put rope on the SW LP8500, Tmax 9000, Smittybuilt 8000, or Warn XD9000 and you've got a very light winch. That explains why I'm not buying a SW EP winch.
Of the lightweight powerful winches listed in paragraph above, the SW LP8500 and Tmax all models (and possibly the Smittybuilt) are the best for adding less heat to drum. Since Tmax has a dangerous remote, and Smittybuilt offers almost no info on their winch, that leaves the SW LP8500 as my best choice for a very light install weight winch that is reasonably rope friendly. If I hope it up by using an EP9 solenoid, then the LP8500 should be really sweet and still light. I would put rope on it. Perhaps fire line or whatever that heat resistant rope is called.