There are really two questions here:
Can grow lights burn my plants?
Can heat from grow lights burn my plants?
The answers are:
Light probably won't burn your plants
Light, even intense light, probably won’t burn your plants. If a plant is getting too much light, it can challenge your crops and be counterproductive, but it won’t actually cause burning.
... but the heat from some lights might.
Some lights, like incandescent, fluorescent, and HID lights have bulbs that get quite hot. Usually, it’s the heat that burns your crop, causing tissue death and crop losses. These lights can basically cook your crops, especially if they are close to the plant like in a compact or high density system.
Of these three light types, fluorescents produce the least heat.
This is one area where LED lighting shines (again). While LED lights do produce some heat, they deal with that heat more effectively than other light types. Plants can grow much closer to LEDs than other lighting types because of this. Usually crops can grow right up to the light without burning. This makes them very convenient in compact systems!