Method for controlling the extrusion of a semifinished product in a tyre building process, said method comprising: providing a semifinished product (1) at the exit of an extrusion assembly (2), said semifinished product (1) comprising at least: a first component (11) made of at least one first material; a second component (12) made of at least one second material, different from said first material; said semifinished product (1) having accumulated heat during an extrusion carried out in said extrusion assembly (2); making a first verification for verifying at least one of: presence of said second component (12) and arrangement of said second component (12) relative to said first component (11), wherein said first verification comprises: detecting first electromagnetic radiations (Rl) representative of a heat emission from said semifinished product (1) while said semifinished product (1) is releasing said accumulated heat; based on said first radiations (Rl) detected, determining first detection parameters (DPI) representative of at least one of the presence of said second component (12) and/or the arrangement of said second component (12) relative to said first component (11); generating a first notification signal (NS1) as a function of said first detection parameters (DPI). An apparatus (100) is also described for controlling the extrusion of a semifinished product in a tyre building process.