No, it isn't.
In the UK Reference Laboratories, we tended just to screen to see if the antibody reacted at 30oC or not. If it did, as per Petz LD and Garratty G. Immune Hemolytic Anemias, 2nd edition, Churchill-Livingstone, 2004, then it was considered to be clinically significant. We would do nothing else at all. The titre of the antibody was thought to be irrelevant, as it was unusual, although not unique, to find a cold auto-antibody reacting at 30oC (or above) that was not a high titre. We certainly did not spend any time at all determining the specificity of the antibody. As I believe I have said before, not only was the specificity regarded as totally irrelevant, but if the specificity turned out to be anti-H, anti-I or anti-HI (as it usually was), we would not recommend the transfusion of Oh units or adult ii units and, as far as I know, there has never been a donor who is both Oh AND an adult ii!!!!!!!!!
In your own case, if the anti-E was not reacting at 37oC, especially with a monospecific anti-IgG reagent, it is not going to be clinically significant, and I really doubt if it was a true anti-E (it is much more likely to be a mimicking anti-E, and I don't blame your Reference Laboratory for one minute for not going on to prove that).