Circuit design - How to fix power supply overheating and reduced performance?
Ohm’s Law tells you it draws 3/0.25=12 A to start and transistor is far too small in power rating to handle cool operation.  The current gain drops towards 10% of hFE as a switch so your base current is under-driven and Rce is 1.5 Ohms
Try &lt;50mOhm Nch 1V=Vth FET instead which is necessary.
Your battery won’t last long either.
If Base =0 Ohms you get slightly lower Vce(sat) and slightly more RPM. It will also slow down with a battery charge. With a CMOS driver ~ 50 Ohm @3V that's (3-0.7=2.3) &gt;&gt; 2.3V/50= 46mA  then you can drive motor best with what you have and run cooler than what you had.  This is OK for the short time you expect.