Hi,
Safety first:
230V on a breadboard? For me a "no-go".
Please don´t do this.
Additionally please use an isolating safety transformer.
***
There is no STW34NM60N in your schematic.
--> To avoid confusion: Please post consitent informations only (pictures, text, schematics...). At least mark unused / modified parts.
So I have to guess that you replaced the IRFP460 with the STWxx.
To calculate the heatsink you need to do first things first.
1) requirements (current, switching frequency, ambient temperature ...)
2) calculate power dissipation (different dissipation types)
3) calculate heatink (using ambient temperature ...)
to the points:
1) current: One may think this simply is 250W/230V = 1.1A. But is this really the case? we don´t know. Mabe the heater is made of PTC or made of metal wire. Example: An 60W incandescent lamp may have the 15 time inrush current (cold filament) compared to the steady current.
2) there is
* ohmic condution loss of the MOSFET during ON time
* switching loss
* maybe diode loss
3) consider: ambient temperature, air flow, closed case ...
Klaus