Study of induced magnetic field is a powerful way to sound Earth internal structure. This work presents a full analysis and interpretation in terms of electrical conductivity and temperature of vector magnetic field measurements from Swarm Level1b data product from 26/11/2013 to 31/12/2019. Time series of the Gauss coefficients associated with the induced and inducing magnetic field are obtained from the data after removal of the core and lithospheric fields models and data selection. A Bayesian inversion of the induced field Gauss coefficients is then performed to obtain a new estimate of Earth's 1D mantle electrical conductivity down to 2000 km depth. This profile is fully compatible with the profiles derived from satellite and ground magnetic observatories data but does not present in the lower mantle the increase predicted by laboratory-based conductivity profile associated to classical mantle composition and temperature profile. Using the most recent database to model the electrical conductivity of all mineral mantle phases, two different methods are used to interpret Swarm data in terms of temperature for a given composition and water content. The first one is based on an interpretation of the conductivity estimates in terms of temperature by classical numerical root search. The second one consists in inferring a temperature probability density function from a Bayesian inversion of the Gauss coefficients associated to the induced magnetic field. Our results show that the later provide more reliable estimates of mantle temperatures, in relation to more physically grounded prior values. This second method provides also tighter constraints on the electrical conductivity estimates of the lower mantle.