It seems alright. Perhaps with a "!" at the end, to make it read more warmly?
Another possibility: A warm welcome to xxx inspection group! It's not incorrect, but I'm not sure it's necessary to include our Institute, since where the group is being welcomed to should be clear from the context.
As written, that is an instruction to the members of the Institute, telling them that they are to welcome xxx inspection group. Warmly is an adverb, welcome has to be a verb, imperative.
GEmatt's alternative is much better (unless of course you meant to post an instruction to the members of the institute).