Suppose two giant planets have the same mass but are located at different distances from the Sun. Temperature measurements reveal that the...

There are a variety of factors influencing this, such as gravity and having a magnetic field. Note also that having the same mass doesn't mean they have the same gravity; a planet composed entirely of iron and a planet composed entirely of ice may have the same mass, but will have very different sizes and surface gravity. 

However, in the simplest model, we would expect the inner planet to have less hydrogen. For one, hydrogen...

There are a variety of factors influencing this, such as gravity and having a magnetic field. Note also that having the same mass doesn't mean they have the same gravity; a planet composed entirely of iron and a planet composed entirely of ice may have the same mass, but will have very different sizes and surface gravity. 

However, in the simplest model, we would expect the inner planet to have less hydrogen. For one, hydrogen is a very light gas, which means it would tend to rise to the top of whatever atmosphere the planet has, meaning that it will encounter the most intense and undiluted photon energy from the sun. These interactions can cause the hydrogen to absorb so much photonic energy that its kinetic energy exceeds the planet's escape velocity. A similar phenomenon is responsible for the evaporation of standing pools of water even when the temperature doesn't exceed the boiling point. This is demonstrated by the fact that the inner planets of the solar system have very little hydrogen, whereas the outer planets, which have exponentially less solar exposure, have a very high proportion of hydrogen in their atmospheres.