Plants generally seem to like bottom heat to help grow roots. My recent experience growing sweet potato slips has led me to believe that tucking the glass inside a black plastic pot and positioning on a sunny windowsill to take advantage of solar heat might also help rooting cuttings like yours.
Increasing the humidity by covering the top with ventilated plastic (just like with starting seeds) should help too. My favorite method is plastic water bottles with bottoms cut off and cap removed. There's usually a right kind of bottle size/design that if you cut it at just the right place, will fit snugly over any container.
The classic horticultural "propagation tray" consists of bottom heat (heating wire) in the bottom of a 6" deep wooden tray filled with moist sand, and overhead misting system. Don't have anything fancy like that myself, but I thought I'd mention it.
BTW, if the mother plant is yours, thyme propagates easily by ground layering -- lay the longer shoots on the ground (or on surface of the soil in same/another pot) and dump some soil over the stem touches the soil. Sever from the mother plant once roots grow along the stem.
Appreciate any input.
