G0ULI
I remember years ago expessing surprise at seeing the police helicopter refuelling at a local flying club and doing a rolling takeoff.
If it had wheels, no big deal. If it had skids ... an interesting day!
The maneuver you describe might be what we used to call
a running take off. Or, a MGW take off. Not sure what it was you saw.
Apparently with the temperature hovering around 30 degrees centigrade, they couldn't take off from their base, only about 250 feet higher but needing a vertical departure with the tanks more than a quarter full.
Gross weight versus DA, versus all other performance factors (to include how much wind and from where) influence the ability to hover in and out of ground effect.
If you can't hover without some droop, do you want to take off? If yes (there will some factors and rules and SOPs that drive that answer) you will want to get a bit of translational lift flowing through the rotor head to reduce power required.
So clearly the weather can have huge effects on performance and I have to conclude that rotor stall would occur at a higher rotational speed in hot weather than on a cold day as just a single practical example of the variables that have to be taken into account.
Do you mean powered or unpowered?
DA influences everything a helicopter does. If your power available versus power required are an unfavorable balance, when you try to lift up into a hover you'll tend to see the NR droop, which is often a good performance flag to put it back down and either get rid of some weight, check that your performance planning didn't have an error, get into the wind ... depends on the situation.
My mentors who used to fly armed Hueys in Viet Nam used to tell stories of having to use an IGE take off run (get some speed and translational lift so they'd have enough power margin to begin a climb away from the forward operating base) when they'd come back to rearm/refuel so that they could actually take off and return to the fight. I am pretty sure SASless and a few others could tell us some real life experiences along those lines.