During the time you have available, advance reservations are essential as the
Camino Frances is very busy during the summer months (June - August). I have used
www.booking.com and booked several days out at a time. This has worked for many.
Make your initial reservations before you travel from home to Spain, so you have a place to stay for your arrival night or two. Also, make advance reservations for the first couple of walking days.
Once you are on the ground, and maybe after the first day walking, assess the situation and make another 3 - 4 days reservations. Repeat as necessary until Santiago.
Also, have a hard reservation for Santiago. This time of year (summer) is especially busy and some weekends find the city sold out of reasonably priced lodgings. Arriving on Sunday night or Monday night is usually the best plan. It is what I try to do.
As regards the heat, anywhere in Spain or Portugal can be very hot during the summer. Nearer the coast, humidity is higher, depending on ocean winds. You seem to be doing all the right things to counter and prevent heatstroke.
The single best thing you can do, beyond what you are already doing, is to get out each morning at first light, not sunrise. First light is the point at which you can see the yellow arrows and your footing before you put a foot down.
Generally, this is about 30 - 45 minutes before actual sunrise. I use the
eltiempo.es+ app to tell me exactly when official sunrise is for the location I am in. Then I back up my start walking and wake up times accordingly.
When walking during any time of the year that I know will be hot, for me, I plan to get up about one-hour before posted sunrise, and to get walking ASAP.
The only way to beat the heat of midday is to avoid it. Get as much distance in before noon. The hottest time of the day is usually from noon until about 6:00 pm.
I suggest that you want to plan to be done walking by noon or soon thereafter. You may have to wait for an albergue to open, but sitting under an umbrella with a cold drink is preferable to struggling with heat exhaustion.
Hope this helps.