There are two issues to consider: the time of year and the time of day.
Time of year for mowing
The answer to the first is simple, as it is really only necessary to mow between March and October. After this, it is likely that the grass will be too wet most of the time and that there is insufficient growth to warrant cutting. In exceptional circumstances, you may want to consider mowing in late autumn and winter if there is a particularly mild spell. The RHS has more advice on this aspect of mowing and on the second factor to consider: the time of day.
Time of day for mowing
In an ideal world, you really don’t want to consider mowing first thing in the morning. Perhaps you are a morning person and would like to get this job ticked off your list before it gets too warm in the summer months, but you are likely to regret it. The payback will be the likelihood of the grass being damaged by the blades and disease spreading more easily with the damp of morning dew.
As Noel Coward famously sang: ‘Mad dogs and Englishmen go out in the midday sun.’ Only a mad dog would consider mowing the lawn at midday. Stress can affect lawns as much as people, which will manifest itself by struggling to keep in moisture and to photosynthesise.
If you have resorted to mowing at the wrong time of day due to time pressures, you may need to give your lawn mower some TLC by investing in Briggs and Stratton parts. It is simple to order through stockists such as https://diyengineparts.com/Brand/1/briggs-and-stratton.
Early afternoon is not an appropriate time either; in fact, ‘midday sun’ really goes on until at least 4pm in the height of summer. The only solution is to don your gardening clothes and get out your mower in the late afternoon or early evening. You will have the advantage of longer days as the months move on, and the grass will have had time to dry out completely. It will also have plenty of time to recover before facing the heat of the sun the following morning.
When gardening, never do in the morning what you could put off until the evening. You will be doing your lawn a huge favour.