The UNFCCC Paris climate meeting of December 2015 committed to holding the rise in global average temperature to below 2.0 °C above pre-industrial levels. It also committed to pursue efforts to limit warming to 1.5 °C. This leads to two key questions. First, what extent of reductions in emissions will achieve either target? Second, given emissions cuts to achieve the lower target may be especially difficult to achieve, then what is the benefit from reduced climate impacts by keeping warming at or below 1.5 °C? To provide answers climate model simulations need to follow trajectories consistent with these global temperature limits. This implies operating models in an invertible form, to make model-specific estimates of greenhouse gas (GHG) concentration pathways consistent with prescribed temperature profiles. Further inversion derives related emissions pathways for these concentrations. For this to happen, and to enable climate research centres to compare GHG concentrations and emissions estimates, common temperature trajectory scenarios are required. Here we define algebraic curves which asymptote to a stabilised limit, while also matching the magnitude and gradient of recent warming levels. The curves are deliberately parameter-sparse, needing prescription of just two parameters plus the final temperature. Yet despite this simplicity they can allow for temperature overshoot and for generational changes where more effort occurs to decelerate warming change by future generations. The curves capture temperature profiles from the existing rcp2.6 scenario model projections, which have warming amounts towards the lower levels of those that society is discussing.