First temps are probably OK (The temp reported in bios is fine depending on room temp). Ideally the core temps should be not more than 9 C above room temp (but this will also depend on the airflow inside your case). Winter time, My room temp is about 20 C - My overclocked I5-750 runs about 30C (core temps in HWMonitor).
disregaured the statement "The Intel manual states it requires an ambient temp of 38 degrees C." ambient tem is normally your romm temp and I dought your room is 38 C.
After you get system up and running. download a program such as CPUID HWMonitor to monitor the 4 core temps. Then run prime 95 for 15 min - if temps hit 70 C before 15 min end test!
Side comment - very few people who normally built there own use the stock intel HSF - While the work they are at the bottom of the heap interms of performance and it is NOT uncommon to have the one of the push pins incorrectly seated.
I do not even install, when I order the CPU I also order a after market HSF. There are some good ones for around $30 - WELL worth it. Myself I prefer one with a backing plate - hate push pins.