Data supporting Lewis et al., 2025. Diffusion-free Dynamics in Rotating Spherical Shell Convection Driven By Internal Heating and Cooling. Accepted for publication in Astrophys. J. Data is output from simulations of internally heated and cooled, rotating, Boussinesq, spherical shell convection. All data is in NetCDF format, and can be opened using the Python package xarray. All data was produced using the code Dedalus. All data has been time averaged over at least one diffusion time. For each experiment (see paper for details), three files are included: EXP_traces_timavg.nc, EXP_profiles_timavg.nc and EXP_phi_avgs_timavg.nc. 'traces' files include scalar quantities integrated over the volume of the domain, or the volume of the 'convection zone' (see paper). 'profiles' files include quantities averaged horizontally over the spherical shell, so that they are a function of radius only. 'phi_avgs' files include data averaged azimuthally, so that there are a function of theta and r. In each case, 'EXP' should be replaced with a string of the following form: 'Ra_X_Pr_Y_Ta_Z', where X, Y, and Z are the flux Rayleigh number, Prandtl number, and Taylor number used for the experiment (e.g., X=9.5e8, Y=1, Z=1e7). Relevant output diagnostics to the paper include: Traces: Re_fluc_cz - Reynolds number computed by integrating the rms fluctuating velocity over the volume of the convection zone. RoU_fluc_cz - 'Bulk' Rossby number computed by integrating the rms fluctating velocity over the volume of the convection zone. Rovor_fluc_cz - 'Vorticty' Rossby number computed by integrating the rms fluctuating vorticity over the volumn of the convection zone. Profiles: b_s2_avg - radial profile of shell averaged buoyancy (the temperature variable in the Boussinesq system) flux_b_tot_s2_avg - radial profile of the shell averaged total heat flux (convection + conduction) flux_b_cond_s2_avg - radial profules of the shell averaged conductive heat flux Phi_avgs: u_phi_avg - azimuthal average of the phi component of the velocity v_phi_avg - azimuthal average of the theta component of the velocity w_phi_avg - azimuthal average of the radial component of the velocity upup_phi_avg - azimuthal average of u'u' (where the prime denotes a departure from the azimuthal average, and u is the phi component of the velocity) vpvp_phi_avg - azimuthal average of v'v' (where the prime denotes a departure from the azimuthal average, and v is the theta component of the velocity) wpwp_phi_avg - azimuthal average of w'w' (where the prime denotes a departure from the azimuthal average, and w is the radial component of the velocity) In each output file, a number of other diagnostics are included. The naming convention for these is by analogy with the convention outlined above.