If the surface mount component could be electrically connected to GND it would be connected using an array of thermal vias. The ground plane then provides heat dissipation across a bigger area so that the temperature stays within reasonable limits. If the power dissipation of the component is quite high, an additional heat-sink is attached on the bottom side of the PCB.
It becomes more difficult when isolation is required between the component and ground. Connecting the component to a heat-sink is still possible using isolating thermal interface materials e.g. SIL-PAD 900S. But thermally connecting the component to the ground plane is not as easy.
This is where thermal jumpers come into play. You can use them to connect the power dissipating component to an array of ground vias while maintaining electrical isolation:
The thermal resistance for a 0612 thermal jumper is about 4°C/W. To gage this performance, we could have a look at the thermal resistance of an array of vias:
Source: High efficient heat dissipation on printed circuit boards
The 5mm x 5mm via array has a thermal resistance that is similar to one 0612 thermal jumper. But at least three 0612 thermal jumpers can be connected to the 5mm width of the via array. This makes the thermal resistance of the vias more significant then the thermal resistance of the jumpers.
Coming back to the original question:
If lets say that we use thermal jumpers in the circuit and they get either short or open during operation. How does it effect my heat performance of the circuit.
Shorting the jumper also means electrically shorting the two nets. This is very likely not a good idea. The concern of an open circuit is the temperature increase of the component. It depends on the component and its power dissipation if this is harmful or not.