Temp, not current, could be the first limiting factor for a TO-220 analogue regulator just plugged into a proto shield without heatsink. 78xx regulators need at least 2volt headroom, and they have a current limit of ~1Amp.
So at max current they dissipate at least 2watt (more if input voltage is >7volt). Enough for a temp rise of ~130C above ambient.
Leo..