Chains converge to different results

@jessegrabowski I’m interested in recreating the results of the paper Global non-linear effect of temperature on economic production by Burke et al, but by learning distributions rather than point estimates in order to have a better idea of the uncertainty of the estimates as well as be able to combine this analysis as part of a larger, Bayesian-network type model. My data comes from the same source as was used in this paper.
Do you think that this approach is for some reason ill-suited for the type of data I am working with? I am new to statistical modeling and so any feedback or comments on this idea/approach is really appreciated and helpful.