summer greeting card; midsummer inquiry after someone's health
A seasonal letter or card sent during the hottest part of summer to ask after someone's well-being. Similar to 暑中見舞い, but 暑中伺い can carry a slightly more formal or polite nuance of 'inquiring' rather than just 'visiting' or 'greeting'.
See also: 暑中見舞い
This year too, we sent midsummer greeting cards to our valued customers.
On a midsummer inquiry postcard, you add words expressing concern for the recipient's health.