where ℏ = h 2 $_{π}$, h is Planck’s constant, and k$_{B}$ is the Boltzmann constant. The barrier heights, V$_{0}$ and V$_{1}$ , are taken to be the maximum energy of the long-range adiabatic potential V ( R ) evaluated in a basis set of partial waves | LM$_{L}$ 〉 [14]. The potential V ( R ) includes a repulsive centrifugal term, ℏ $^{2}$L ( L + 1) / (2 µR $^{2}$) where µ is the reduced mass of the colliding molecules, an attractive isotropic van der Waals interaction − bC$_{6}$/R $^{6}$, and the dipolar interaction. We use only two fit parameters, b and γ , when fitting this model to the measured β/T vs. d . The solid lines in Fig. 4 are a fit of the measured time evolution of n , T$_{z}$ , and T$_{x}$ to the numerical solution of three differential equations (see Supplementary Information): Here, we have allowed for a difference in the average energy per particle in the two trap directions, “ T$_{z}$ ” and “ T$_{x}$ ”, so that β = K$_{0}$T$_{z}$ + 2 K$_{1}$T$_{x}$ . For the fits, we fix the d -dependent coefficients K$_{0}$ and K$_{1}$ using the previous fit to the inelastic loss rate data in Fig. 1. In addition to heating due to inelastic loss, we include a measured background heating rate of c$_{bg}$ = 0 . 01 µ K/s. The elastic collision rate in Eqns. 4 and 5 is given by Γ$_{el}$ = nσ el v N $_{coll}$, where the elastic collision cross section σ$_{el}$ is a fit parameter, v = √ 8 k B ( T z +2 T x ) 3 πµ , and the constant N$_{coll}$ can be thought of as the mean number of collisions per particle required for rethermalization. We use N$_{coll}$ = 4 . 1, which was computed for p -wave collisions [30], however, we note that N$_{coll}$ depends on the angular dependence of the scattering and may be somewhat different for dipolar elastic collisions. dn dt = − ( K$_{0}$T$_{z}$ + 2 K$_{1}$T$_{x}$ ) n 2 − n 2 T$_{z}$ dT$_{z}$ dt − n T$_{x}$ dT$_{x}$ dt (3) dT$_{z}$ dt = n 4 ( − K$_{0}$T$_{z}$ + 2 K$_{1}$T$_{x}$ ) T$_{z}$ − 2Γ$_{el}$ 3 ( T$_{z}$ − T$_{x}$ ) + c$_{bg}$ (4) dT$_{x}$ dt = n 4 ( K$_{0}$T$_{z}$ ) T$_{x}$ + Γ$_{el}$ 3 ( T$_{z}$ − T$_{x}$ ) + c$_{bg}$ (5) [1] Krems, R. V. Perspective: Cold Controlled Chemistry. Phys. Chem. Chem. Phys. 10 , 4079 (2008). [2] DeMille, D. Quantum Computation with Trapped Polar Molecules. Phys. Rev. Lett. 88, 067901 (2002). [3] Andre, A., DeMille, D., Doyle, J. M., Lukin, M. D., Maxwell, S. E., Rabl, P., Schoelkopf, R. J., Zoller, P. A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators. Nature Physics 2, 636-642 (2006). 12