Yes. Too many windows facing south in an ordinary house can cause over heating. A window area on the south side of not more than 6 per cent of the total floor space of your house (counting a heated basement) should cause no problems. More than that and you have created half a solar house -- lots of heat but no control.
Passive solar houses have to incorporate special heat control measures to take advantage of the sun while avoiding radical temperature changes inside the house:
-- Thermal mass is needed to hold and smoothly distribute the heat.
-- Thermal shutters keep the heat in when the sun goes down, but inside the house they tend to cause moisture problems on the glass. Exterior thermal shutters work with fewer problems.
-- Air circulators distribute the heat throughout the house.
-- Summer shading (leaf trees and/or roof overhang) blocks the sun from these same windows during the summer.
If you are presently stuck with a house with too much south-facing window area, you could increase the mass of the room it shines on by adding one or more layers of heavy drywall to the wall that receives the direct sunlight. Heavy tile floors will do little good in Canada as our winter sun rarely even shines on the floor. You could increase afternoon ventilation from the hot room to other parts of the house. Alternatively, you could simply shade or close off a window.