Merely getting a better CDP probably ought be your focus. A superior player might or might not necessarily sound 'warmer' per se, but it should offer improved resolution, extension, dimensionality, tone color, dynamics, and textural refinement, with less congestion, all of which should make it more involving and pleasant to listen to. The Thiels will reveal the quality of whatever they're fed, and to this end the integrated amp, and whatever player you choose, might benefit from addressing issues of power conditioning and/or power cords in the system if you haven't already.
But Wlutke is right in bringing up that since the little 1.6's (which I think sound great BTW) can't offer the most generous lower-frequency balance, even if you don't feel the want or need to experiment with subwoofers (and assuming your room isn't too big for these speakers), it sounds like you might at least consider revisiting the topic of speaker and listening chair positioning, because as he implies changing CDPs alone isn't going to affect this particular impression (tonal balance) as much by comparison. Thiels do require certain set-up parameters in terms of listening distance and distance to sidewalls if they're not to sound bright, so if you have any questions in this area you should let us know your layout.
But Wlutke is right in bringing up that since the little 1.6's (which I think sound great BTW) can't offer the most generous lower-frequency balance, even if you don't feel the want or need to experiment with subwoofers (and assuming your room isn't too big for these speakers), it sounds like you might at least consider revisiting the topic of speaker and listening chair positioning, because as he implies changing CDPs alone isn't going to affect this particular impression (tonal balance) as much by comparison. Thiels do require certain set-up parameters in terms of listening distance and distance to sidewalls if they're not to sound bright, so if you have any questions in this area you should let us know your layout.