They get pretty warm but they don't get hot enough to melt plastic... unless they're surrounded by plastic, then there's nowhere for the heat to go.

Does ballast get hot?

A further test would be to check for heat from the ballast. Ballasts usually run hot, about 140 degrees F, but if one is so hot that you can't keep your hands on it, it is likely the culprit. ... An overheating ballast can become hot enough to ignite combustible ceiling tiles or any other combustible it contacts.

Does HID lights get hot?

HID lights can reach very, very high temperatures (far in excess of what a halogen can achieve). ... They can be uncomfortable to touch after being used, but they don't reach the 100 – 300 degree temperature range common for even low-end headlights.