Ion Petroianu, VA3NOI
So, last night I did some meaurements.
Room temperature at 18 °C. LM7805 goes as high as 52°C with 13.8V at power feed.
Temperature drops to 49°C when at 12.8 V (that is the votage of a fully charged lead acid battery)
Temperatue rise of 34°C. If you will enclose the board and ambient temperature is summer hot you can expect temperature of the case to get close to 100. A heat sink will be required.