Joule Lamp

[Lynxsteam]

Fluorescents are always harder on this circuit.  I had my best CFL success with the first version of this device.  Brads then confirmed the exact number of turns for fluorescents (something like 32:680).  See earlier in this thread.  Diameter of the aircore may play a role.  Yours is a little bit bigger diameter than what we tried.  I think with the larger diameter you are not confining the field inside the tube as well.
I use 7.5 watt warm LEDs by Utilitech Pro.  These bulbs have circuitry inside that is helping make this simple circuit work.  Avoid Philips LED bulbs, there is something about them that is designed for 60 hz sine wave and it is a power hog on the oscillator.  Interestingly Philips bulbs will run of 12 vDC.
I don't experience transistor heating unless I am running 8 or more bulbs.  Get out of the reverse bias mode if you can.  Maybe rewind the toilet paper tube on something similar to what was first shown in this thread.
Are you  just experimenting? or are you wanting to achieve something specific?

[rxpc]

Thanks Lynxsteam,

I'm just experimenting with this circuit right now, and used what I had available to make the coil. As it is, it's great, but for
1 CFL bulb, adding more bulbs I can't get the brightness as with 1 bulb. I plan on making a larger one with PVC, it'll help with the windings. Heavier wire and rewinding is taking it's toll on the little toilet paper roll. 

I didn't have the transistor heat up as much until I lowered the primary windings, I'll go back to the 20:1 primary winding,
and see if that helps keep the transistor cooler.

[Lynxsteam]

rxpc,

Go back and look at B-rads video for clues on how to light fluorescents. http://www.youtube.com/watch?v=XmVt1sPbUdQ

Also note he followed the original design very closely.  The original design on this thread was for modded cfl's.  Later in this thread we started changing the design considerably to light the LED bulbs.  Perhaps the transistor heating is happening because you are using the LED design to light CFLs.
B-rads also noted that to start the CFLs takes more amperage but once warmed up the amps can be dropped.  This is usually done with a starter or ballast.  I think we can do this with the aircore by starting with fewer turns tapped.  Attach two wires to the primary - one at say 30 turns, another at 40 or so.  Once the bulb is started remove the tap at 30 turns.  This may also help in lighting several CFLs. 
Once you experiment with this, you may find that there are ways to use one design for different bulbs.  A double throw switch connected to different primary taps might accomplish this.  In the later versions I was using three layers of secondary to select low and high power.  Another clue is that the primary for CFLs was not tightly wrapped and was not closely spaced.  In some cases the primary only covered part of the secondary.  Again I think B-rads replication was the best insight.

[gadgetmall]

unmodified cfls .. 5 volts http://youtu.be/8_0OsJUNlgw

[Lynxsteam]

Gadgetmall-

Very nice video and great experiment!  I can light that same 40 watt unmodded CFL on the LJL aircore but I have the turns setup for 12 volts.  I find 12 volts is more common.  I can also change out for the LED and about the same brightness on a 60 watt incandescent as you are seeing.  But I also notice that you are doing some experiments that would indicate you are lighting these bulbs at very low amps.  Keep going and keep sharing.

I have been doing some experiments with a wind turbine alternator directly connected to the LJL circuit.  I have a 35 volt electrolytic capacitor smoothing the input voltage.  It takes very little with one finger turning the alternator to light the LED bulb.  I am hoping that this circuit can perhaps be a benefit to the small wind field.  Wind is tough because the power output changes from moment to moment by as much as a factor of 10x.