Is the warm air the same temp as ambient??
i.e. if it is cold outside, is the air delivered cold and if it is warm outside, the air delivered is warm?? Or is it warm regardless of ambient??
If it is warm regardless of ambient, then the heater valves aren't closing properly - as you have replaced the heater valves with new, you can discount the valve being the issue so must be a wiring to the valve issue causing the valve on the affected side to remain slightly open. IIRC the valves are normally open and the HeVAC powers them closed as necessary.
The valves have been known to stick, or a spot of crap can gather under the valve seat causing it not to close fully....but if yours are new, this also may not be the issue.
The air movement within the heater box flows through the heater matrix regardless of set temperature, the heater valves allow coolant into the matrix to warm it if necessary, the matrix is split in two halves for the passenger and drivers side.....so the only way to get warm air out of the heater is for coolant to be getting into it......the two halves do share a common return line piped into the manifold on the back of the engine.
It is a longshot, but if you have a hole in the matrix the flow can come back through the return into the affected side of the matrix - this happens because on a 100% working system the valve is closed, the coolant can't flow back into the matrix as it would need to displace the cold coolant already in there......but if the matrix has a hole in it, this then allows the hot coolant from the return to displace the cold coolant through the hole in the matrix making it warm and thus warm the air.
I am in the process of changing my matrix as I had issues with one side being a different temp to the other by a marginal few degrees....and then I was getting air locks in the matrix that were difficult to bleed out. Then came the losing coolant and I couldn't figure out where from.....
I then static pressure tested the system and the pressure would drop over a few minutes but could not for the life of me find out under the bonnet where it was coming from......until I saw a dribble of water under the car.
Fearing this was the rear manifold (common item to crack and leak coolant) I crawled under and the dribble was from the passenger side A/C drain......The car hadn't been driven or started for 2 days so it was not condense, tasted it.....bugger coolant. The only way for coolant to be coming from the A/C drains is if the matrix has a hole in it!
I disconnected the pipes to the matrix and tee'd them together to complete the circuit and have been running the car for the last 2 weeks or so while I figure out how to get the Matrix out....the official procedure is to strip the interior and remove the whole HeVAC unit.....but I feel it *may* be possible to just remove the matrix with the unit in place (see my threads) - this I will be attempting over the Bank Holiday weekend shortly!
I would advocate doing a pressure test on the system and see if you have a leak....hope you don't, but your symptoms are scarily like mine were!