Thyme plant does not need fertilizer very often as fertilizer can burn its roots, since it is very sensitive. However, if you see that the quality of the soil is very poor you can add the fertilizer to the plant.
If the quality of the soil does not improve as the plant grows, you should add fertilizer to the plant. Even in that case the plant will need fertilizer only once in a month. So if you feel there is a need for the fertilizer, you can add it after a gap of a month.
Do not add excessive quantity of fertilizer. Since the plant is very sensitive at its roots, the fertilizer can potentially burn the roots. So it is always recommended to add fertilizer in very light quantity.
Instead of adding fertilizer in its original or in powder form, you should use liquid form of fertilizers for these plants. Liquid fertilizer works quickly and efficiently, and the plants get the energy it needs timely and then the impact of the fertilizer is vanished.
If you are not using fertilizer in a grain form, water plant after adding the fertilizer to it. This will make the fertilizer absorb into the plant soil completely and at once. Leaving fertilizer as it in the plant's soil can damage its roots. When you water the plant, it works quickly.
Mulching the soil around the plant on a regular basis is necessary for its healthy growth. Generally, you should mulch the soil before adding the fertilizer to it, and after that water the plant. This helps the fertilizer ease into the roots area of the plant and helps its growth.
Generally, you should inspect the soil before adding fertilizer to it, and if you feel there is really a need for fertilizer then add it. Otherwise, fertilizer is not recommend, especially too often for the plant. It can grow on its own.