This work proposes a multi-Fickian method to analyse the hygro-thermal behaviour of timber bridge elements under Northern Europe climates. A temperature-dependent wood hysteresis is included in the model and the thermal effects due to temperatures above and below zero are taken into account. As a case study, the model is used for the hygro-thermal simulation of a glulam beam of Älsvbacka bridge in North of Sweden that was monitored by using wireless sensors in a previous study. The model, implemented in Abaqus FEM code, is able to predict the states of moisture and temperature in protected parts of the beam by using as external loads the relative humidity and temperature of the air provided by in-situ measurements. Furthermore a simplified model using a wood hysteresis independent of temperature is found to provide similar results and appears easier to implement in finite element codes.