Thanks for playing!
There isn't actually a friendly fire mechanic - most likely, your tanks just overheated as they were shooting. The gray bar beneath a tank indicates how much heat it has; you need to prevent it from filling up or it'll overheat and start taking damage.
Although in hindsight, you do have a good point. The heat mechanic was pretty poorly designed compared to everything else. If I could do it again, I would probably redesign the heat mechanic to be more forgiving, or just omit the heat mechanic entirely - it just wasn't worth it for the wild card.
Yeah, there's a part in the tutorial talking about how tanks overheat if they drive or shoot too much. This isn't really that big of a problem later on though, because bigger hulls have much better heat tolerance. So once you unlock them, you can do a lot more before you have to stop and let your tanks cool back down.
