[ 0014 ] fig1 and fig2 a through 2 g show , as exemplary embodiments of the present invention , a sensor element 10 of a so - called lambda probe having a measuring region 15 and a supply lead region 16 . sensor element 10 is constructed as a layer system and has a first , second , third and fourth solid electrolyte layer 21 , 22 , 23 , 24 . on first solid electrolyte layer 21 a first electrode 31 is applied on an outer surface of sensor element 10 in measuring region 15 , and it is coated with an electrode protective layer 33 . electrode protective layer 33 may be designed to be porous , so that first electrode 31 is exposed to a measuring gas surrounding sensor element 10 . on the side opposite first electrode 31 of first solid electrolyte foil 21 a second electrode 32 is applied . second electrode 32 is positioned in a reference gas chamber 34 put into second solid electrolyte foil 22 . reference gas chamber 34 may be filled with a porous material . in order to heat measuring region 15 of sensor element 10 , a heating device 40 is provided between third and fourth solid electrolyte layers 23 , 24 , which has a heater 41 that is electrically insulated from the surrounding solid electrolyte layers 23 , 24 by a heating insulation 42 . heater 41 and heater insulation 42 are surrounded on their sides by a sealing frame 43 , which , for example , may be made of an ion - conducting material . in one example embodiment , heater 41 may not be , or at least not fully electrically insulated from surrounding solid electrolyte layers 23 , 24 , or heater insulation 42 may be brought right to the side surfaces of sensor element 10 , so that sealing frame 43 may be dispensed with . on the outer surface of fourth solid electrolyte layer 24 , a heat conducting layer 51 may be applied , for example , by a screen - printing technique . heat - conducting layer 51 is coated with protective layer 52 , also , for instance , by a screen - printing technique . heat - conducting layer 51 is made of platinum , and has a thickness of 5 to 50 μm , e . g . 12 μm . the protective layer is made of a ceramic material such as al 2 o 3 , zro 2 or of a mixture of al 2 o 3 and zro 2 , and has a thickness of 10 to 100 μm , e . g . 30 μm . in fig2 a through 2 g , exemplary embodiments of the present inventions are shown . a top view of fourth solid electrolyte layer 24 and heat - conducting layer 51 is shown , protective layer 52 not being shown so as to make clearer the position of heat - conducting layer 51 . protective layer 52 is arranged so that heat - conducting layer 51 is completely covered . the position of heater 41 , which is positioned not on the outer surface of sensor element 10 , but in the layer plane between third and fourth solid electrolyte layers 23 , 24 , is shown in fig2 a by dotted lines . the position of heater 41 in fig2 b through 2 g corresponds to the position of heater 41 in fig2 a . in the exemplary embodiment shown in fig2 a , heat - conducting layer 51 completely covers measuring region 15 and the transition region between measuring region 15 and supply lead region 16 of sensor element 10 . in the exemplary embodiment shown in fig2 b or 2 c , measuring region 15 or the transition region , respectively , are covered . [ 0019 ] fig2 d shows an exemplary embodiment in which heat - conducting layer 51 is provided in the region of the edges of the outer surface of fourth solid electrolyte foil 24 . in the exemplary embodiment shown in fig2 e , heat - conducting layer 51 has strips arranged in a star shape , which run from the center of measuring region 15 of the outer surface of sensor element 10 to the edges of the outer surface , and thereby may make possible a temperature adjustment between the center and the edges of the outer surface in measuring region 15 . the exemplary embodiment in fig2 f represents a combination of the embodiments of fig2 d and 2 e . in the exemplary embodiment shown in fig2 g , heat - conducting layer 51 has a grid - type structure . heat - conducting layer 51 may be brought right up to the edge of the outer surface of sensor element 10 without formation of a separation from the edge . it may also be provided that heat - conducting layer 51 has a small distance from the edge of the outer surface , and that protective layer 52 fills the gap between heat - conducting layer 51 and the edge , and thereby covers heat - conducting layer 51 also on its sides . the distance of the heat - conducting layer from the edge may need to remain so small that no substantial temperature gradients may arise in the edge region . this may be safely ensured if , for example , the distance of heat - conducting layer 51 is not greater than 0 . 5 mm . it should be pointed out that the arrangement , according to the present invention , of heat - conducting layer 51 on an outer surface of sensor element 10 is not limited to the special type shown in fig1 but may be generally used for sensor elements in which mechanical tensions appear at the outer surface , on account of temperature gradients . in a further exemplary embodiment , several of the outer surfaces of the sensor element may be furnished with a heat - conducting layer .