There is another more fundamental process at work as well.
The oils left in your fingerprint also contain body salts and a host of other chemicals. There is a substantial amount of energy departing a halogen filament that is in the infrared region of the spectrum.
I would venture that most halogen bulbs have a quartz envelope. Quartz is virtually transparent to infrared light. If you cause any part of the quartz to become opaque, (i.e., leave a fingerprint on it) it is no longer able to transmit the infrared component of the optical spectrum and that energy is absorbed by the “glass” of the bulb.
The concentration of heat promotes a process known as “vitrification”. This drives a cascading reaction in the envelope of the bulb that causes a non-uniform or localized build-up of heat in one area of the lamp’s globe. The thermal stress involved can eventually shatter the bulb.
This same exact mechanism manifests in large “bell jar” type epitaxial reactors used in the semiconductor industry.