= Solution
Motion toward incoming <cosmic microwave background> radiation produces a blueshift. The photon occupation function of a <blackbody> depends on $h\nu/(k_BT)$, so the same Doppler factor multiplies both <frequency> and effective <temperature>. Looking forward along the Sun's <peculiar velocity>, one obtains
$$
T_{\rm forward}=T_0\sqrt{\frac{1+\beta}{1-\beta}}
\simeq T_0(1+\beta),\qquad \beta\simeq300/(3\times10^5)=10^{-3}.
$$
Taking the mean <cosmic microwave background> <temperature> as about $2.73\,\mathrm K$ gives
$$
\boxed{\Delta T_{\rm forward}\simeq2.7\,\mathrm{mK},
\qquad T_{\rm forward}\simeq2.733\,\mathrm K.}
$$
The numerical total inherits the rounded mean temperature; the robust estimate is the positive millikelvin dipole increment.
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