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We aim to reproduce the DCO$^+$ emission in the disk around HD163296 using asimple 2D chemical model for the formation of DCO$^+$ through the colddeuteration channel and a parametric treatment of the warm deuteration channel.We use data from ALMA in band 6 to obtain a resolved spectral imaging data cubeof the DCO$^+$ $J$=3--2 line in HD163296 with a synthesized beam of0."53$\times$ 0."42. We adopt a physical structure of the disk from theliterature that reproduces the spectral energy distribution. We then apply asimplified chemical network for the formation of DCO$^+$ that uses the physicalstructure of the disk as parameters along with a CO abundance profile, aconstant HD abundance and a constant ionization rate. Finally, from theresulting DCO$^+$ abundances, we calculate the non-LTE emission using the 3Dradiative transfer code LIME. The observed DCO$^+$ emission is reproduced by amodel with cold deuteration producing abundances up to $1.6\times 10^{-11}$.Warm deuteration, at a constant abundance of $3.2\times 10^{-12}$, becomesfully effective below 32 K and tapers off at higher temperatures, reproducingthe lack of DCO$^+$ inside 90 AU. Throughout the DCO$^+$ emitting zone a COabundance of $2\times 10^{-7}$ is found, with $\sim$99\% of it frozen out below19 K. At radii where both cold and warm deuteration are active, warmdeuteration contributes up to 20\% of DCO$^+$, consistent with detailedchemical models. The decrease of DCO$^+$ at large radii is attributed to atemperature inversion at 250 AU, which raises temperatures above values wherecold deuteration operates. Increased photodesorption may also limit the radialextent of DCO$^+$. The corresponding return of the DCO$^+$ layer to themidplane, together with a radially increasing ionization fraction, reproducesthe local DCO$^+$ emission maximum at $\sim$260 AU.

Exploring DCO$^+$ as a tracer of thermal inversion in the disk around the Herbig Ae star HD163296