Solenoid driver heating issue
Only difference is the TCM has the low side switching whereas this
  schematic has high side switching


Erm, no. This schematic has low side switching (Q3 is connected to ground). And


  The schematic diagram of the driver is very similar to the below
  image.


is not true either. That schematic is not remotely going to work. Since you don't seem to know how transistors in general work, I'm not able to explain it in the course of an answer here.

I'll give you  a starting point though. Assuming that the circuit is designed using high-side switching (and the use of a PNP is a clear indicator that this is so), the schematic should look something like







simulate this circuit &ndash; Schematic created using CircuitLab

and your Q3 is not possibly an FMMT549 - those are SOT-23s with a maximum current of 1 amp.

As Jasen has answered, your circuit (as drawn) is going to get hot.

Assuming that your actual circuit looks more like mine, I suggest you check for a wrong value on the 47 ohm resistor (it may be too high) or replace Q1.

Another possibility is that Q2 is being partially turned on, with the result that Q1 collector is forced to be more than the ~0.5 V or less which it normally uses to turn on the solenoid is raised to something higher and the base drive to Q3 is reduced. If this is so, Q1 is getting hot, too.

Much more important, provide a real schematic. You seem to have taken an existing schematic and reworked it according to your (mistaken) ideas about how these things work. So until you provide an accurate schematic any suggestions are really just us trying to second-guess you.

Here's a hint - if there really is a high-side/low-side difference between circuits, Q3 needs to be an NPN, not a PNP. And all the rest of the circuit needs changes as well.