Airman.... I though you were they one asking....
I just say that you need a current limiting at the transistor base....
And if you want to avoid two resistor just connect the two grounds of the LEDs together and then use resistor...
I don't know about heat up.... doing that I guess you need a 1/2W resistor....
you can also do the same with the anode... like this....
transistor --> resistor ---> LEDs ---> ground....
That's the more normal thing to do....
I don't really understand why you get drawn in a spoon's water.... really...
It's simple....
How many Watts your LED are? What is the maximum allowable current through the LEDs?
W = VI where W are Watts, V is volts, I is current....
You have a let's say 30mW LED with a 5V supply right? then you get the amps from the equation above!!!
Then... Ohm Law!!!! R = V / I.... you have I and you have V.... So you get the resistor needed!!! Simple!!!
If you have two LEDs then by the second Kirchhoff's law about current splitting, you get that
if one LED is 30mW then two same LEDs are 60mW!!! and calculate the resistor again.... which should be the half...
You don't have to worry, about burning your LEDs cause you can possibly imagine that their resistance is almost the same...
Thus equal currents should go through them...
EEehhhh..... I hope this helped you....
Regards, Lefteris
Greece