I have over 75 years of Model A ownership and have driven in countless parades. I have never seen a Model A boil over, but slow parades with participants walking have caused cars of the 50's era to boil over. If your car performs well as a daily driver or on long tours it will be OK in a parade. Do not ride the clutch, do not tailgate, do not retard your timing control very much and you will be OK. The biggest hazard I encounter is occupants in cars in the parade throwing candy to kids. The kids run out to pick it up and create a hazard. In my area throwing candy can get you removed from the parade in some jurisdictions as the risk to the children is considered very hazardous. It also disturbs the flow of the parade as cars behind candy tossers slow down, then go a bit faster to catch up. Parade gaps are caused. My hometown of 3,000 population had 65 old cars in last year July 4th parade, a typical amount as no pre registration is required, so we drew many participants from out of town.