I doubt that there will be a heat problem. That driver board looks like your typical AMC7135-based board. If you drive your light using 1xLi-ion, the driver will run quite efficiently. The LDO regulator efficiency is roughly Vout/Vin (since quiescent current is essentially negligible). I've measured about 3.4V at 1000mA forward current to a P4. Thus, your driver efficiency might start out at 3.4/4.2 (81%), quickly go to a quasi steady-state 3.4/3.7 (92%), and finish at 3.4/3.5 (97%) before falling out of regulation. By then, the Li-ion will be mostly depleted anyway. Worst-case, at 81% efficiency, the driver is wasting only about 0.8W as heat.
Although the ideal is to provide separate heat sinking for the LED and the driver, a Mag mod heat sink is probably massive enough (plus it is in good thermal contact with the Mag tube for additional heat sinking) that you could use some thermal epoxy and pot the driver to the LED heat sink. Plus, the P4 is pulling only about 3.4W of power, of which about 2.7W is dissipated as waste heat. So that's a total of only about 3.5W max of waste heat to manage.
The high powered quad dies like the P7 and MC-E generate a lot more than that in waste heat.
of course 5 years later it still works, with cruddy old leds in it.
