The choice of rubber material used in DC accessories as joints is a delicate task as the stresses to support resort to both capacitive and resistive distribution, and the thermal gradient set during cable operation further modifies the stress distribution. Field distributions in a model HVDC joint are computed in nonstationary electrical and thermal conditions considering different thermal conductivities and different electrical conductivity laws for the joint material. Results obtained mainly on the tangential field distribution at the dielectric/dielectric interface are discussed. Imposing an electrical conductivity substantially higher in the rubber compared to XLPE has positive impact on the field under the stress cone. However, it is counterbalanced by field enhancement near the central deflector. The strengthening of non-linear effects in the joint contributes to relaxing the field at hot points near the deflector. The impact of thermal conductivity is also evaluated. The results provide orientation for defining appropriate physical properties of joint material for a given cable insulation.