Based on your symptom it may not be the climate control unit. Mine was doing the same thing and I sent the CCU to Brian for rebuilding. He said it looked like it had been done before but he went through it anyway. Didn't fix the problem. There's also a resistor unit installed on the side of the fan housing and that can go bad too, and when it does this is the result, high speed only. Brian had me remove mine and send it to him for testing (@ no charge) - turned out to be bad and he doesn't rebuild them. There are some threads on replacing a transistor but Brian said it's not normally successful. A new part fixed the problem. I can post more but my NSX records are on another computer.
OK - Transistor Assembly, P/N 79340-SL0 A01, paid $226. Also replaced the fan motor, P/N 79310-SL0-A02, $190, because Brian said when the transistors go bad the motor isn't far behind, and a new transistor will fry if you don't replace the motor too. There was a TSB on this for some early cars - fan motor drags and overloads the transistor. I can probably find more info if you need it but there's info in the Prime wiki or faqs or somewhere.
Climate control failures are much more common then failure of the power transistor so blindly changing it is a waste of time and money. The service manual had a procedure for checking the signal to the power transistor to see if its there. If the signal is present then the power transistor is bad and as noted if it has failed the blower motor is bad too. If the signal is not there then the climate control needs repair or replacement.
Correct me if I'm wrong but I also thought there was a high and a low speed relay... Mine failed and I swapped the relays and it now will kick on later than usual but still works.
I have a simple fix for this problem but I need to be able to buy the connectors for the power transistor. It's a 3 pin plug/socket that mounts behind the fuse box under the hood. I've got photos but there are no markings other than A-1 (arrow character?) 3, on the socket. I don't want to dammage the dash by removing the CC unit. I've read the procedure and it's pretty involved. I'm an EE and my solution is an in-line wire harness with a wireless receiver that will drive the power transistor from a key fob. It also can be done with a simple snip of a wire but most folks don't dig that. I put a connector in the middle of the power transistor harness and inserted my circuit there, but removing the power transistor to install the connector is more than most people would want to do also, so the plug-and-play solution would be best. Anyone know where to get the conns?