The photo on this page shows the miniature thyme tree beginning to form a thicker canopy, planted opposite the fairies and the miniature curry plant (silvery leaves) in a shallow drawer organizer which is being used to create a herb garden for a windowsill. (The ground cover beginning to grow over the rocks is another miniature ground cover thyme, Thymus serpyllum 'Minor' Click on the photo for a larger, clearer view.
This photo was taken two to three weeks after the bushy thyme received its initial pruning. You can see how more and thicker side branches are forming as the tips of each branch are pinched when new growth develops.
Once you are satisfied that your bush thyme is beginning to thrive again and take on a miniature tree shape, rub all the side shoots and leaves off the main branches below where you are training your tree canopy. You can do this by rubbing them off gently with your fingers. Continue to do this until the bush has healed the scabs formed where the buds were on the branches which form the 'trunks' , and is putting all its efforts into growing branches in the young growth you are creating at the top of the plant with your pinching of the new shoots to thicken the growth.
As you grow your tree, analyze what shape you want it to have. If you notice shoots in useful places, leave them to grow and pinch them into a new canopy section growing out from the original ones. If the shoots are growing so they cross other growth, or sprouting from the bottom of the plant, rub them off with your fingers while they are still small and green.
If you didn't place your thyme into its permanent container, do so as soon as you are satisfied that it is recovering from its heavy pruning. You don't need to prune the roots like a bonsai to keep the bush small, just make sure you are growing it in sandy, poor soil without much in the way of compost. Don't fertilize it. Struggle will cause it to send out more shoots, and thicken up the main branches faster than the soft growth you will create with fertilizer. Control the shape through pinching it on a regular basis, and let it grow to a mature size (eight to ten inches tall for most bushy thymes.)