Can heat when sleeping raise heart rate such as being hot from the blankets or covers and furnace?

Generally Not: Heart rate goes up in normal people by about 10 points per degree of temperature elevation, but that's "core" (internal) temperature which is extremely hard to raise in the absence of disease. The body has spent 50, 000 years learning to cool itself, and does so with great efficiency, so it's not usually a blanket alone causing this. That said, overheating is never a great idea.

Thanks for asking!: Yes, when your body is warm, and your muscles are lying still, your blood vessels will dilate. This increases the space your blood volume fills. The preload, or filling of your heart will decrease which will increase your heart rate.