  We consider the asymptotics of the discrete heat kernel on isoradial graphs
for the case where the time and the edge lengths tend to zero simultaneously.
Depending on the asymptotic ratio between time and edge lengths, we show that
two different regimes arise: (i) a Gaussian regime and (ii) a Poissonian
regime, which resemble the short-time asymptotics of the heat kernel on (i)
Euclidean spaces and (ii) graphs, respectively.
