Black Hole Mass Accretion Temperature

[purple_wave]

Hey everyone,
I have a quick question. I have to find out how hot a cloud of material falling into a black hole would become. I have a hint that it is due to the gain in kinetic energy the material experiences as it falls in, but I'm not sure how to relate the two. Also, I have to find the peak wavelength that would radiate if the material emitted as a blackbody, but I'm assuming I can just use Wein's law once I know the temperature.
Thanks!

 

[purple_wave]

I just thought of something,
could I use the relationship 1/2m(v)^2 = 3/2kT to find the temperature from the kinetic energy?

 

[Chronos]

Boltzmann's law appears more appropriate.