Consider this sentence:
- The ventilation system will still work, but without a capability of cooling.
You can indeed say, for instance, He has the capability of performing first-rate work. In the sample sentence above, however, the expression is a direct translation of …une capacité de refroidissement. The use of the the little word a throws it all off in English.
So, you could at the very least go with …but without the capability of cooling. But to give your English text its own true flavour, write something like …will still work, but won't be able to cool / but won't provide cooling / but without cooling capacity.