Cessna 525 Captain reported a loss of speed; and unable to maintain altitude; after climbing to 45;000 ft. when temperature was higher than standard. The Captain immediately requested a lower altitude with ATC; descended; then continued the flight.

Narrative

I filed for FL450. This is very common for us to do in the CJ3 and normally it is not an issue. I was cleared to FL450 and was climbing uneventfully through FL430. I noticed ISA was higher than forecast and I was not climbing as well as normal. I asked the controller for the block 430 to 450 to enable my climb. He said he was unable the block due to traffic at FL430; so I needed to descend to FL410 or he said I could have FL450 if I could make it in six minutes. I was at 43;200 ft. at this point so only needed 300 ft. per minute. I decided I could easily accomplish this at that low climb rate. Unfortunately; when I achieved FL450 I was too far behind the thrust/drag curve; and I was losing airspeed even after level off. I knew I was not going to be able to maintain FL450. I notified the controller immediately and he gave me a vector and a descent to FL410. He gave excellent callouts to myself and the other aircraft. No TCAS directives were received by my aircraft and I don't believe any were by the other aircraft; although I am not sure of this. The closest callout from the controller was 5 miles I believe. The controller did an excellent job. I have learned a valuable lesson from this experience. When we first started flying this aircraft; I always filed to FL410. I would then level off and gain some airspeed and then go up to FL450 no problem at all. The aircraft is so good at climbing I realized I did not need to do this and could go right to FL450. Unfortunately; heavy and well above ISA; this is not always the case. I plan on going back to filing FL410 when we are taking off at; or close to; max gross weight.