bulb voltage heat relationship

It's not the voltage of the bulb, but rather the total power consumed by the bulb, which is all converted to heat.  You want bulbs that have a lower current draw at the voltage you're operating at, that will generate less heat.  You can also look into the LED replacements for the bulbs, that would totally solve the issue.

When tungsten lamps are run at less than their rated voltage, they emit more heat, percentage-wise, than light, on a sliding scale.  That's not really an answer that will help you find the right lamps, but is an interesting aside to your problem that might explain wuzzhappnen.

LED's would seem to be the best choice for replacements, as they are for a lot of applications these days. Less power draw, less heat, longevity, etc.

As John said, reducing the voltage does reduce the heat in a bulb.  The question is "Does a 2447 bulb draw less power than a 1447 at 18V?"  I found some unlabeled test data that seems to indicate that at 18 volts, the power difference is 2.7W vs. 3.5W.

Although your 022 switches operate briskly on 18V, a good 022 should work at 14-15 volts.  With the 2447 you would have 1.8 watts and approximately 40% less heat at 14V.  (I say approximately because light bulbs aren't a constant resistance value.)

Try an 1819 bulb. It's rated 28 volts and 40ma. At 18 volts it uses only 25 ma which is a little less than half a watt. When I replaced the 4 bulbs in passenger cars an 8 car string of cars went from 6 amps to less than an amp of power consumption.

An 1819 is the wrong shape.  That is a long cylindrical bulb, not a spherical bulb.