[evan_au]

(Dark Matter) doesn't seem to clump and seems to avoid the inner areas of galaxies

The hypothetical subatomic Dark Matter particles would accelerate under the effects of gravity as they approach the center of a galaxy, and decelerate as they leave.
In an elliptical orbit around the galactic center, they spend most of their time traveling slowly, far from the center of the galaxy.

How does (Dark Matter) get hot in the first place?

It seems likely that many Dark Matter particles would have been formed in the Big Bang.
As space expanded, they would have separated into different groups traveling at different velocities.
Now they have been gravitationally captured by galaxies (or, more accurately, clumps of Dark matter have captured enough visible matter to form a galaxy).

Another possibility is if Dark Matter particles can be created in high-energy collisions today (eg by cosmic rays or the LHC), they would be created with far more energy than relic dark matter particles from the big bang, and could escape from our galaxy.

How hot is a x-ray hot (star)?

Most X-Rays are from the accretion disk of hot gas spiraling into a black hole, neutron star or white dwarf star.
Although the Sun's surface temperature is only around 6000C, the Sun's Corona can reach temperatures of a few million degrees, hot enough to emit X-Rays.
Solar flares can also emit X-Rays.
See: https://en.wikipedia.org/wiki/Astrophysical_X-ray_source#Sun

[Professor Mega-Mind]

      Question for your question .
Suppose Dark Matter IS particle .
Suppose it has mass , and long-range gravitational attraction to other masses . Suppose moreover that it has a shorter-range repulsive force for other masses .  Would that not explain the odd astronomical observations we observe , while also explaining   why we cannot find actual  physical interactions of DM , nor get our hands on it .  The field-strength ratios would determine whether BHs could draw them in close enough to ingest . 
Alternatively , DM may not be a particle at all . It may be an aspect or a phase change of the space-time matrix itself .  It could still evidence the above behaviors , however , and affect the very matter & energies that it is host to.
Alright , time to ingest lunch !..P.

[Professor Mega-Mind]

...................Addendum .
The above applies only if DM turns out to be an actual particle , with actual mass .  If it is not cogent , but is a product of the space/time matrix itself , then it is unlikely that black holes consume that in which they are imbedded .  Such would have powerful consequences and effects , none of which has been observed as of yet .
Probably not , and it would be a black hole anyway .
P.M.
Ref.- Compare and contrast the above , with the newly pro-pounded "Vainshtein Theory" .      Sauce for the goose , eh ? 

[Kryptid]

Relevant to this topic: https://www.livescience.com/63977-axion-stars-form-quickly.html

[Professor Mega-Mind]

Dude , that theory has so many bandages that I'm calling it "The Mummy" !  It also has so many "ifs" I'll have to change that to "The Iffity-Mummy" theory ! 
I don't believe that such an absurd Dark Notmatter could really exist , let alone go unnoticed . I also don't believe that , under any realistic conditions , this "Magic Dust" would clump up to form stars .  Seen any kugelblitzes lately ?
P.M.

[Kryptid]

For those who don't know what axion particles are: https://en.wikipedia.org/wiki/Axion