So I just bought a Hegel H390 and

First, if at all possible do NOT use the 15x15 room — it’s an absolute nightmare from a bass perspective (I know because I had that exact size room years ago). I heard Joseph Audio Pulsars (original version) with Hegel electronics and the sound was sublime. Not too warm, not too cool, just sounded like music with outstanding imaging/soundstage, and they’d work well in your room. Just one option, and best of luck.

A fantastic speaker you can get around $10 k or less
the Latest Marten trio from Sweden they can compete with speakers if much higher cost a true Bargain and quality built throughout.

Tannoy Arden?

+1 soix      
A square room (15x15) will be difficult to impossible to tame the bass nodes. The speaker choice should be your's and your's alone. Many will work well with your Hegel but try to find one that satisfies your listening tastes. You'll have to get out and do some comparative listening and don't forget that a speaker will never sound the same in your room as it does anywhere else. Good luck!

Pretty hard to go wrong with something from Sonus Faber,Dynaudio or Dali..  Not a big fan of Dali but the Sonus and the newly designed Dynaudio are very nice.

The Hegel I would not say is a warm sounding amp.  In fact in comparing it to the old BEL Audio amp recently, the Bel being a very good class A amp was more musical and warmer sounding.

Depending on your musical tastes, look at a used pair of Vandersteen 5As, Verity Audio, and Ascendo speakers as I have seen very good used prices on there speakers.  The newer Ascendo speakers are excellent if you can find them.

Happy Listening.