Thermal radiation would indeed be an issue, but there are a couple of interesting facets of this question and its answer that are obscured by the hyperbole. It's instructive to peel away the hyperbole to learn more.
First of all, "millions of degrees" is not compatible with "metal" in any familiar sense. Iron boils at 2862°C. Tungsten melts at 3422°C and boils at 5930°C[1]. At millions of degrees you would have an expanding plasma ball competing with its own thermal radiation to explode and kill you. We could postulate that something confines the plasma, and in that case the thermal radiation would cook you in short order, as explored in other answers.
However, I think your friend may have been thinking of a very real phenomenon that often gets obscured by introductory physics curricula. I don't see it mentioned here, but it has literally and metaphorically burned many people, so it's worth re-casting the question in order to highlight this phenomenon.
"If you wave your hand near a block of 660°C Aluminum, just below its melting temperature, do you feel the heat, assuming convective heat transfer is negligible?"
We are familiar with hot objects in everyday life, and we intuitively expect hot objects to radiate heat. The Stefan-Boltzmann law tells us how much power per area a blackbody radiates, and many objects in our everyday lives are decently approximated by blackbodies. 184
Under the assumption that the Aluminum behaves like a blackbody -- which you should now be highly suspicious of -- you might intuitively expect to feel approximately the following power/area of radiated heat when you wave your hand past:
$$ \frac{P}{A}=\sigma T^4\approx (5.67 \cdot 10^{-8})(273+660)^4 \approx 4.3 W/cm^2 $$
You would feel only 3% of that. You might erroneously assume that the Aluminum has a low temperature, touch it, and burn yourself. Many have.
The reason is simply that many materials under many conditions don't behave like black bodies. Aluminum is a notorious outlier. The ratio of actual emitted thermal radiation to black body radiation is called thermal emissivity and varies quite a bit for different materials, surface finishes, and so on:
https://en.wikipedia.org/wiki/Emissivity
In the lab, this has practical consequences. You can't read the temperature of shiny metallic surfaces through a thermal camera because those surfaces will behave like mirrors, not temperature-indicating glowsticks. You can fix this problem by adding little black patches to any shiny parts you need to measure.
I startle myself at least once a year by assembling a circuit, watching it through a thermal camera for the first powerup, reaching over to turn on a power supply, and jumping back at the sudden jump in temperature due to seeing my arm's thermal reflection in the shiny components.
[1] Taken directly from the wikipedia pages for Iron and Tungsten. I believe these temperatures assume vacuum but didn't verify that. Regardless, I wouldn't expect P=1atm to fundamentally alter the discussion. 580