Usually not an issue of stuff getting too hot this time of year as long as everything has adequate ventilation and water. If it's too humid/wet you can get a real fungus problem. As long as your temp. is below 100F, you're probably OK. Are you using enclosed seed-starting containers? Where are they? Outdoors in full sun? Covered in some way (under glass/plastic)? Some more information would be helpful in assisting with your situation.

My understanding of Winter sowing is that it's done in open flats in the Fall and they're just left outdoors through the Winter and allowed to germinate naturally in the Spring. Is this what you've done, or something different?