I believe what constitutes 'warmth' is subjective. I have owned several NAD amplifiers throughout the years and have listened to several others. I would not declare them to be, as a class, warm, however in comparison to the A-S701 it seemed to me that the NAD 356 was more so. I might have declared the 701 as more airy, lighter. Since warmth has much to do with the speakers in use, I should add that this comparison was made with a pair of B&W CM5s.
I also owned the NAD 326BEE prior to the NAD 356BEE, made the change because I was using them in a secondary system for outside use and the slight extra power (headroom?) provided by the 356 proved beneficial. Other wise I would have kept the 326. I agree with jrpnde that is was 'more musical'.
I have also listened to and enjoyed PSB speakers, most recently Synchrony 1s. And have heard that NAD mates well with PSBs. I have not heard then together however. I do believe NAD provides the amplifiers for PSB subwoofers.
At the moment, if I was considering the purchase of a new integrated having both phonostage and DAC, at a budget limit of $1600, I am not sure what I would purchase. If wanting to stay closer to $1000 budget and purchase a new product, I would consider the A-S801 or the Outlaw receiver (forgot model). There are likely more contenders. That said, I would most likely look at purchasing a used recent model integrated which retailed at ~$2500 for somewhere between the aforementioned price points with the features required.