Removing R2 would increase the chances for thermal runaway, there are two "loads" on R1, one is R2 and the other is the transistor. If one "load" is removed than the voltage goes up. If R2 is removed then the voltage Vcb goes up and so does the current Ib. (you could also think of it from a current node perspective and the current through R1 must go through R2 and the transistor, if R2 is removed all the current goes through the transistor, which is a simple way to look at it but it sill works) This would increase current through the transistor because Ib would be higher and so would Ic.

But thermal runaway is independent of this. If you heat up a resistor, the resistance will change a bit (usually in ppm) but this normally doesn't produce a noticeable change in current. 

The power dissipated in a transistor is based from Ic. So if you heat up a transistor, you get *more current* through the collector. This can be bad because this causes the part to heat up more, and more current to flow through, and more heat. 

This is why it's important consider the thermal runaway effect and make sure you've considered the changes in beta over temperature. A good idea would to find the max temperature for the design in the datasheet and also consider what would happen if it increased Ic. 


Here is an example of how current gain changes in a real transistor with temperature (the 2n3904). At certain currents (like 10mA) Ic would increase with the temperature increasing. The good thing is the designers accounted for the thermal runaway effects and at higher currents, beta/hFE goes down with temperature at higher currents which reduces the thermal runaway effect. In other BJT's, this may not happen. The most important thing is to avoid reaching the absolute maximum temperature of the part.

[![enter image description here][1]][1]
Source: https://www.onsemi.com/pub/Collateral/2N3903-D.PDF


Edit:

> Since there is R2 which provides a path to ground, would Ico still
> flow through base-emitter junction or flow through R2 to ground?
> Because, to me if it flows through R2 it wouldn't cause thermal
> runaway. (?)

I think the confusion is that for a PNP this would be true, since we have an NPN. If R2 is removed we have more Ib if R1 is the same in both circuits, more Ib means more Ic and more Ie. This would *increase* the temperature of the part and wouldn't necessarily cause thermal runaway but could cause thermal runaway by starting the cycle. It would depend on the parts in the circuit. 

[![enter image description here][2]][2]

Now if we start from the circuit without R2 adding R2 would *decrease* the chances for thermal runaway.

No portion of Ie (what you call Iceo) flows through R2 with an NPN. The directions of currents are indicated above. 

> Since there is R2 which provides a path to ground, would Ico still
> flow through base-emitter junction or flow through R2 to ground?
> Because, to me if it flows through R2 it wouldn't cause thermal
> runaway. (?)

No portion of Iceo flows through R2. All of Iceo flows through Re

  [1]: https://i.sstatic.net/N3HKm.png
  [2]: https://i.sstatic.net/I99nv.png