Eitri couldn't find the intended handle for Stormbreaker, so Groot held Stormbreaker and chopped off his arm as the handle of the axe.
I'm going to be calculating how hot Stormbreaker was when Groot wielded it, and I'm going to do so using Newton's Law of Cooling.
T(t) = Temperature of Stormbreaker at time t
T(0) = Initial temperature of Stormbreaker = 3422 degrees Celsius (I'm going to assume the melting point of tungsten)
Ta = Ambient temperature (temperature of surroundings) = 30 degrees Celsius (I'm assuming this because although they were close to a neutron star, no one mentioned being hot and they didn't look very sweaty)
The rate of change of the temperature dT/dt is proportional to T-Ta (Newton's Law of Cooling).
Since T>Ta, the derivative dT/dt should be negative.
dT/dt = -k(T-Ta) where k is a positive constant
Let y(t) = T(t)-Ta
Differentiating y(t) we get dy/dt = dT/dt = -ky, since Ta is a constant and therefore its derivative is 0.
If you've learnt about exponential growth and decay you'd know the solution to this is y(t)=y(0)e^kt.
Plugging in y=T(t)-Ta we get
T(t)-Ta = (T(0)-Ta)e^-kt
T(t) = Ta+(T(0)-Ta)e^-kt
Assuming the axe starts being exposed to air where Eitri breaks open the chest or something, the time it cooled before Groot held it is 27 seconds, or 0.45 minutes.
At 1:27 Eitri exposes the axe to air and at 3:00 when Stormbreaker starts killing the Outriders we can see it it is no longer glowing. I'm going to low-ball this and say that Stormbreaker has already cooled to 20 degrees Celsius, room temperature.
20 = T(1.55) = 5+(3422-30)*e^(-1.55k)
We can solve that k = around 3.49749.
Then we plug in t as 0.45 to get the temperature when Groot held it
5+(3422-30)*e^(-0.45*3.49749) = 707.96316 degrees Celsius
Eh, not bad. Expected higher though.
I can calculate the amount of radiation energy and conduction energy, but that will yield underwhelming numbers, probably around a thousand Joules at best.