Neuroanatomically speaking I think Kahneman may be talking about the "hot" and "cold" executive function pathways (this wikipedia article is fairly informative on the subject). Hot executive function is thought to involve affect or reward processing, and the ventromedial prefrontal cortex is generally thought to be crucial for this. Cold executive function is thought to be invoked more by abstract tasks with little reward involvement, and is associated with the dorsolateral prefrontal cortex.
This extract from Prencipe et al. (2011, cited below) has more to say about the cognitive modeling of this theory--the article is from a developmental standpoint, so it speaks specifically to children and adolescents.
Rather than considering executive function (EF) in hot and cool situations in a dichotomous
fashion, this characterization recognizes the interplay between
relatively hot aspects of EF and relatively cool aspects of EF
(Cunningham & Zelazo, 2007). According to this model, information is
processed hierarchically, with relatively quick evaluative reactions
followed by the generation of approach–avoidance-oriented responses.
These relatively simple responses may suffice, or, if necessary,
further processing and reprocessing of information may ensue that
allows reflection on context and future consequences, and that
supports the top-down control of behavior. The extent to which a
reflective response is likely to be generated depends on a number of
factors, including time, motivation, and neural and cognitive
maturity. Given that neural development also proceeds in a generally
hierarchical fashion, with areas of the brain associated with more
complex processing developing later than areas of the brain associated
with more automatic processing (e.g., Bunge & Zelazo, 2006), children
and adolescents may be expected to be less reflective than adults.
Moreover, difficulty in generating reflective responses is likely to
be most evident in emotionally charged situations that have meaningful
personal consequences; in these situations, emerging cognitive control
must be implemented in the context of potential interference from
relatively automatic responses to potential rewards and punishments.
I haven't read "Thinking Fast & Slow" but I would in general be pretty skeptical of claims that there are two "systems" for thinking; it is a bit more accurate in my view to say that these are two capabilities that can be brought to bear on a situation, and most situations will involve some combination of both. In addition, I have never heard any evidence that there are processing-speed differences between hot and cold.
Prencipe, Angela; Kesek, Amanda; Cohen, Julia; Lamm, Connie; Lewis, Marc D.; Zelazo, Philip David (2011). "Development of hot and cool executive function during the transition to adolescence". Journal of Experimental Child Psychology 108 (3): 621–637. doi:10.1016/j.jecp.2010.09.008. ISSN 0022-0965.