Knocking under any acceleration or just moderate to heavy acceleration?
If the knocking is random rather than regular, I would check the condition of the engine mounts. A failed front mount could allow the engine to be moving back and forth during acceleration resulting in the noise. Perhaps check the mount anyway just because it is 'easier' to do and rule out as a contributing factor.
If the knocking is regular, I agree with 8R6 that the axles are a potential candidate. First thing, put the car up on a hoist or jack it up so that you can do a visual inspection of the in board and out board boots on the half-shafts. If the boots are torn or there is visible leakage of grease from the boots, then the shafts need to come out for maintenance which may consist of boot replacement / grease repacking or replacement of the joints. While the shafts are out you can test them for radial play - fix one end in a vise and rotate the other end to check for radial movement. Ideally I think there should be no radial movement - I don't recall seeing any limits or test procedures in the service manual for that.
If visual inspection of the half shaft boots does not identify any problems, you can still do a 'sort of' radial play check. On a standard transmission car this is easy to do by jacking one rear wheel off the ground, other wheel remains on the ground and put the transmission into first gear with the emergency brake off. Try to rotate the raised wheel and listen for clunking. Repeat for the other side. On the manual transmission cars it can be difficult to differentiate drive shaft noise from the ever present transmission lash so it may be necessary to make provision to visually check for movement in the driveshaft while doing the test. I know zip about the auto and whether they suffer from the drivetrain lash and I am presuming that engagement of Park should suffice to lock the transmission for the test.
If the drive shaft radial play test comes back as zero, while the wheel is up in the air, remove the wheel and then try moving the hub forwards and backwards looking for movement and listening for noise in the suspension joints / pivots. With the wheel back on the hub, try rotating it and listen for noise which might indicate a bad wheel bearing (although bad bearing usually howl rather than clunk). Try the push - pull on top - bottom of the wheel to see if you can induce movement which also might indicate a bad bearing or wear in suspension components.
Honda sells the parts to replace boots and repack the tripod joints. However, if you have rotational play in the drive shafts because of tripod wear, I don't think any amount of grease repacking is going to fix that problem. Others who have done a drive shaft 'repack' on NSX shafts can advise on that. If you have one tripod joint that it toast, Honda does sell the individual tripod joints (not cheap). As far as I can tell Honda does not sell the internal parts for the tripod joints. Note that if the damage to the tripod is on the driveshaft spline where the spider is mounted a new tripod joint is not going to fix the problem. However, I would expect that type of damage to be less common.
There are rebuilt drive shafts available. The few comments on Prime that I have seen about rebuilt drive shafts leave me a little cool on using them as a repair option. There is a company called Insanshafts that lists new high performance drive shafts for the NSX at a lower price than Honda. I have no experience with them. Perhaps others can advise on their experience with them.
I have no clue as to why the hot versus cold might be a contributing factor.
