Heated MOSFET with LED strip
The MOSFET is acting as a source follower and therefore, the voltage it develops at the source is somewhat less than the voltage applied at the gate. So, if T2 collector can produce (say) 12 volts then T3's gate receives 12 volts and T3's source will be a volt or so lower at 10 or 11 volts (maybe even lower with some FETs).
This means that the power dissipation in the MOSFET is quite high because it is dropping 24 volts to around 10 volts at maybe around half an amp. The current is a guesstimate based on what current the LEDs are taking with 10 volts applied. If 0.5 amps flow then the MOSFET power dissipation is around 14 volts x 0.5 amps = 7 watts.
Solution: move the LEDs to the drain and connect the source to ground and now you will fully activate the FET and get 24 volts across the LEDs.