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In this paper we consider a minimal extension to the standard model by ascalar triplet field with hypercharge $Y=2$. This model relies on the seesawmechanism which provides a consistent explication of neutrino mass generation.We show from naturalness considerations that the Veltman condition is modifiedby virtue of the additional scalar charged states and that quadraticdivergencies at one loop can be driven to zero within the allowed spaceparameter of the model, the latter is severely constrained by unitarity,boundedness from below and is consistent with the di-photon Higgs decay data ofLHC. Furthermore, we analyse the naturalness condition effects to the masses ofheavy Higgs bosons $H^0$, $A^0$, $H^\pm$ and $H^{\pm\pm}$, providing a drasticreduction of the ranges of variation of $m_{H^{\pm}}$ and $m_{H^{\pm\pm}}$ withan upper bounds at $288$ and $351$~GeV respectively, while predicting an almostdegeneracy for the other neutral Higgs bosons $H^0$, $A^0$ at about $207$~GeV.

Naturalness in Type II seesaw model and implications for physical scalars