Is a diode an effective way to replace a resistor in an application where heat should be avoided?
Bulbs have a high PTC ratio from 300'K to 2500'K to 3000'K 

measure the string R value to obtain the cold R per bulb, I expect it to be 1/8 to 1/10th of 14.1 Ohms.

Due to this huge PTC range , the bulbs tend to operate in a constant current with the addition or subtract of a few bulbs while the voltage across and power changes according to these changes in voltage drop but at relatively the same current.

Thus when you add a linear R to the string, the overall power remains the same roughly for small changes so removing or adding a small power R does not affect the total P, as the bulb voltage drops a bit, cools down lowers its R and thus keeps the current about the same. It acts like an INrush current limiter (ICL) which operates at 160'C or thereabouts intended only for limiting surge start currents,  These were once used on 100W bulbs to extend the life but cost as much to make as the bulb.

Using the diode however switches off the voltage and power by 50%
If this reduced power is acceptable consider reversing the diode in one string to balance the load current.