I think a mahogany body will sound warmer than an ash or alder one, for sure.
As for Thinlines.... I've never tried a mahogany one but I have an ash one. I believe the hollow construction emphasises the highs and lows, there's less "focus" to the sound than there is with a solidbody - it can sound sweet if you pick gently, surprisingly harsh if you pick hard. I don't gig, so I've only played at low/home volumes - I don't know how it would behave at stage volume.
In general, if you play rock I think you'd probably be better served by a solid than a thinline.
There is another option - a chambered rather than thinline body. The body's still partially hollow, but it's more like a honeycomb, so it's less "acoustic" than a Thinline. It behaves more like a solid, but with lighter weight and a bit more resonance.
http://www.warmoth.com/Guitar/Bodies/Tele/ChamberedTele.aspxIf you want your Tele to be "as warm as a Tele can be", are you considering different
neck woods? You could go for a mahogany body
and mahogany neck, maybe. And get a modern six-saddle bridge with a thick baseplate, that'll help kill the "Tele twang"!
