Hot: If it's hot, the molecules of gas near the top of the atmosphere are bouncing around a lot. Sometimes they bounce right out into space, and if they are going fast enough they may not come back. So hotter means that the atmosphere may be lost -- especially the lighter elements.
Gravity: The minimum velocity something has to have when leaving the surface of a planet in order to entirely escape from the planet is called the escape velocity.
For example the escape velocity from Earth is about 11 km/sec. There is a simple relation:
vesc2 = const. x M/R
where M is the mass of the planet and R is its radius. (The constant is 2G where G is Newton's gravitational constant, but we won't use that.)
We can conveniently use this by comparing to the earth.
For example, if a planet has a mass equal to 2 times the mass of the earth and a radius equal to 3 times the radius of the earth, then
(vesc)2 ~ 2/3 x (vesc,Earth)2 ~ 0.7 (vesc,Earth)2
An important example is the moon. The moon has a mass equal to (mass of Earth)/80 and a radius equal to (radius of Earth)/3 so
(vesc)2 ~ 3/80 x (vesc,Earth)2 ~ 0.04 (vesc,Earth)2
The escape velocity from the moon is so much smaller than from the earth that it's no wonder that the moon can't keep an atmosphere!
What if a planet had a mass equal to 10 times the mass of the earth and a radius of 3 times the radius of the earth. Would that planet do better or worse than the earth in holding an atmosphere?