Which is the cheapest plastic that retains its structure at 85 °C or higher temperature?
The melting point is not going to give you the answer you want.  To properly select a polymer you need to look at the glass transition temperature $(T_\mathrm{g})$.  This is the temperature at which a material loses crystallinity and starts to more easily flow.  This parameter varies widely with thermal history and internal stress of a polymer material and can be raised by annealing.  

Based on UV resistance, I would exclude any olefin or vinyl polymers as well as ABS.

For water resistance, I would exclude cellulose polymers and acetals.

Based on the temperature requirement I would say polystyrene ($T_\mathrm{g} = \pu{100^\circ C}$), acrylics $(T_\mathrm{g} = 85 - \pu{165^\circ C})$, polycarbonate ($T_\mathrm{g} = \pu{135^\circ C}$), or PPE/PPO ($T_\mathrm{g} = \pu{215^\circ C}$) have sufficiently high $T_\mathrm{g}$'s to remain as acceptable for the mentioned specifications.