If the demand isn't rational (for example, actual need for physical shelter), it doesn't require a lack of supply for a market to become overheated.

Markets can be very strongly affected by greed and mass delusion, an actual lack of supply is not required to drive prices up significantly. You could have a fun pedantic argument over that last statement if you don't want to differentiate on the different kinds of demand, but my point is that demand can vary dramatically with little change in underlying fundamentals - human emotion is more than enough.