Force laws definitely change; thermodynamics probably does too.
Forces (like gravity) fall off in proportion to the square of the distance because the surface area of a sphere in three dimensions increases in proportion to the square of the radius. If we lived in a space with 4 spacial dimensions, they would fall off in proportion to distance cubed because the surface area of spheres in 4 dimensions increase in proportion to the radius cubed. In general, if we lived in a universe with N spacial dimensions, the forces would fall off in proportion to distance^(N-1).
To understand why force laws depend on surface areas of spheres, imagine photons (or any force carrying particles) radiating from an object. Now draw a sphere around that object, and take a snapshot of all of the particles on that sphere. Say you do this at time t1. Now if you follow those particles, you will find that they travel in straight lines away from the radiating object. Because they are traveling in straight lines away from the radiating object, they will always still form a sphere so long as they are all going the same speed (which things like photons tend to do). So if you take another snapshot of those tracked particles at a later time, t2, they will still form a sphere. However, the density of the particles gets reduced; you have the same number of particles distributed over a larger sphere, so the force drops off in proportion to the relative areas of those spheres. If the radius of the sphere at time t2 is r2, and the radius of the sphere at time t1 is r1, then the density has been reduced by a factor of (r1/r2)^2; i.e. it drops off in proportion to (distance traveled by the force carrying particles between times t1 and t2)^-(N-1).
I feel like the laws of thermodynamics would also change, but I'm a little rusty so I'm not 100%. The reason I feel like this is likely is because thermodynamics depends on how many microstates (specific arrangements of particles) correspond to a given macrostate (thing that can be measured from that arrangement of particles). If you change the number of spacial dimensions, then you (should) change the number of available microstates for a given macrostate.