The phrase "temperature slope" refers to how quickly the temperature changes over a certain period of time. It indicates the steepness or gradient of the temperature change. Full definition
One has to go back further than that to obtain a positive temperature slope. (realclimate.org)
(A «positive snowfall temperature slope» in this discussion means that snowfall increased as temperature increased; negative means the reverse.) (tamino.wordpress.com)
As explained above the linear temperature slope results because the air is mixed quasi-adiabatic in the troposphere. (notrickszone.com)