So i asked a question about if the sun was hotter on the inside or the outside, and you said normal stars are are hotter as you go toward the center, so that made me wonder, Are there are abnormal stars that aren't hotter as you go down?
Perhaps I should have said that all
stars increase in temperature as you go inward. However, for normal stars, the temperature increase is fairly rapid in most regions, as described in the previous reply. For 'dead' stars (white dwarfs and neutron stars), there is also a rapid increase in temperature in the outer layers, but once you reach the 'degenerate' interior, the temperature increase, though still present, is much smaller and to a first approximation their deep interior has constant temperature. Even for those stars, however, there is some temperature increase as you go downwards, because if the temperature did not increase, heat would flow inward until the temperature did
increase as you go inward.
The only exception is black holes. Since the entire star has collapsed to a zero-size 'point' mass called a singularity, insofar as temperature has any meaning for such an object, it is the same temperature everywhere in that single point.
There is also a small caveat in that what really
must increase as you go downward is brightness, not temperature. Inside the star, no matter what kind of star ('live' or 'dead'), the only way to increase the brightness is to increase the temperature. But above the surface, in the 'atmosphere' of the star, brightness is increased by increasing the density, not the temperature. So the atmosphere can be (and often is) hotter than the surface. However, being very low in density, its total heat is very small, no matter how high its temperature. And in the case of a question like yours, it would generally be assumed that you start at the 'surface' and go down, and ignore what is going on in the atmosphere, so in my initial reply I ignored that. (If you would like to see how this works in more detail, refer to The Brightness of the Sun at http://cseligman.com/text/sun/sun.htm#brightness
I have to head to the airport in just a few minutes, so though I've done a quick check of the above, there may be some spelling or grammatical errors (or worse). If so, please accept my apology, particularly if any of this is unclear; and continue to feel free to ask followup questions.