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Changes are huge, I would recommend to re-derive the pipe flow rate with a (linear) temperature dependent formula for viscosity and density. You'll get $Q(T)$, from this can get the heat flux and thus will have a nonlinear differential equation for $T(x)$, which you can integrate numerically. Then find the intercept of $T(x)$ with desired outlet temperature. ...


Usually the properties are taken at mean temperature (and pressure) between in- and outlet, often by iteration. If your problem is that sensitive to changes in thermal properties I would calculate the problem sectionwise to account for the non-linearity. When calculating Nusselt Numbers, often the wall temperature needs to be taken into account as well. ...

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