A warm day? How "warm" was it?
Were you guys wearing riding pants when you felt this hot breeze? I noticed when I wear mesh riding pants and am stuck in traffic, that the engine puts out more heat than I think, it's just that my normal riding pants shield better from that heat, so I don't notice it then.
If the fan was coming on normally and you don't see coolant overflowing into the reservoir, there is no problem with the cooling system. IIRC, on the Mk1 the fan is off-set a little to the left. Is it the same on the Mk3? I would expect more heat to come out on the side the fan was off-set to, when it turns on, especially in standing/slow moving traffic.