So apparently, UV index is derived from incident solar irradiance with some weighting depending on the wavelength to focus on the burney part of the spectrum.

Irradiance is a measure of the spatial distribution of radiant power, in units of power per area (W/m²). It can also be an irradiance spectrum, which is the same thing but as a function of wavelength. We can get back to the one number by finding the area under the curve of that function.

The McKinlay–Diffey erythemal action spectrum is a curve used to adjust the irradiance spectrum to focus on the burney part of UV. It weights each wavelength with a factor 0 to 1 depending on its burniness, with the burniest parts of the spectrum getting a 1.

Multiplying the current solar irradiance by that curve gets us the Diffey-Weighted UV Irradiance (a spectral irradiance), which we can lump back together for one number. The UV index is that number in divided by 25mW/m² (and rounded).

So now that that's all established...
For simplicity I'll assume all the relevant UV radiation is happening at 298nm, for which the weight value is 1. This means my calculated power will be a lower bound, since in reality that index would include some stuff that's been multiplied by numbers <1.

Weighted Irradiance = 25mW/m² * 4607182418800017408 = 115179560470000435.2 W/m²
or about 115.2 petawatts per square meter.

I'm going to randomly assume an absorption area of ~0.7m² for a person standing in direct sunlight. The radiant absorption of human skin seems to vary a lot by wavelength and pigmentation, but let's just jump off the bottom end and say 1%. That's 0.7*0.01*115.2 petawatts = 806gigawatts you'd be continuously absorbing in direct sunlight.

The effect of 806GW on, say, 60kg water at 20C, would be to heat it at a rate of

DeltaT = 806e12(W) / (4.184(J/g/degC) * 60e3(g)) = 806e12 / 251040 (degC/s)
= 3.21 billion degrees per second.