  A large portion of the baryons at low redshifts are still missing from
detection. Most of the missing baryons are believed to reside in large scale
cosmic filaments. Understanding the distribution of baryons in filaments is
crucial for the search for missing baryons. We investigate the properties of
cosmic filaments since $z=4.0$ in a cosmological hydrodynamic simulation,
focusing on the density and temperature profiles perpendicular to the filament
spines. Our quantitative evaluation confirm the rapid growth of thick and
prominent filaments after $z=2$. We find that the local linear density of
filaments shows correlation with the local diameter since $z=4.0$. The averaged
density profiles of both dark matter and baryonic gas in filaments of different
width show self-similarity, and can be described by an isothermal single-beta
model. The typical gas temperature increases as the filament width increasing,
and is hotter than $10^6$ K for filaments with width $D_{fil} \gtrsim 4.0
\rm{Mpc}$, which would be the optimal targets for the search of missing baryons
via thermal Sunyaev-Zel'dovich (SZ) effect. The temperature rises significantly
from the boundary to the inner core regime in filaments with $D_{fil} \gtrsim
4.0 \rm{Mpc}$, probably due to heating by accretion shock, while the
temperature rise gently in filaments with $D_{fil}< 4.0 \rm{Mpc}$.
