Using archival X-ray observations and a lognormal population model, we estimate constraints on the intrinsic scatter in halo mass at fixed optical richness for a galaxy cluster sample identified in Dark Energy Survey Year-One (DES-Y1) data with the redMaPPer algorithm. We examine the scaling behaviour of X-ray temperatures, T-X, with optical richness, lambda(RM), for clusters in the redshift range 0.2 <z <0.7. X-ray temperatures are obtained from Chandra and XMM observations for 58 and 110 redMaPPer systems, respectively. Despite non-uniform sky coverage, the T-X measurements are > 50 per cent complete for clusters with lambda(RM) > 130. Regression analysis on the two samples produces consistent posterior scaling parameters, from which we derive a combined constraint on the residual scatter, sigma(ln) (T) (vertical bar) (lambda) = 0.275 +/- 0.019. Joined with constraints for T-X scaling with halo mass from the Weighing the Giants program and richness-temperature covariance estimates from the LoCuSS sample, we derive the richness-conditioned scatter in mass, sigma(ln) (M) (vertical bar) (lambda) = 0.30 +/- 0.04((stat)) +/- 0.09((sys)), at an optical richness of approximately 100. Uncertainties in external parameters, particularly the slope and variance of the T-X-mass relation and the covariance of T-X and lambda(RM) at fixed mass, dominate the systematic error. The 95 per cent confidence region from joint sample analysis is relatively broad, sigma(ln) (M) (vertical bar) (lambda) is an element of [0.14, 0.55], or a factor 10 in variance.