In　the　offset　press,　ink　flows　in　the　microchannel　made　of　two　rotating　rollers　that　are　in　the　state　of　squeezing　and　contacting.　The　ink　flow　characteristics　are　not　only　influenced　by　the　viscous　dissipation　effect,　but　also　change　with　the　heat　transfer.　First,　by　summarizing　the　common　viscosity-shear　rate　models　of　non-Newtonian　fluid,　the　power　law　model　was　chosen　for　describing　offset　ink　through　rheometer　measuring.　Combined　with　the　experimental　data,　the　viscosity-temperature　relationship　of　the　offset　ink　was　described　by　the　Arrhenius＇s　law.　Then,　the　temperature　characteristics　of　the　offset　ink　fluid　in　the　microchannel　were　studied　using　the　fluid　simulation　software　FLUENT.　The　ink　fluid　temperature　field　model　considering　viscous　dissipation　and　heat　transfer　was　established,　and　the　temperature　distributions　of　the　ink　fluid　inside　the　microchannel　and　at　the　exit　and　entrance　were　obtained.　The　influence　of　the　feature　size　on　the　ink　temperature　was　also　researched.　Finally,　the　ink　temperature　and　flow　characteristics　were　compared　with　that　under　the　condition　without　heat　transfer.　We　got　the　influence　of　feature　size　and　heat　transfer　on　the　ink　temperature　characteristics.　As　the　feature　size　is　smaller,　the　ink　temperature　increase　from　the　microchannel　entrance　to　the　exit,　increases　first　and　then　decreases,　and　keeps　invariant　at　last.　The　heat　transfer　makes　the　viscous　dissipation　weaken　relatively　and　then　the　ink　temperature　decreases.　In　a　word,　the　heat　transfer　enhances　as　the　feature　size　decreases.　The　results　provide　reference　for　improving　the　printing　quality　of　offset　press.