It would be a good idea to start by checking with your father's doctor to make sure your dad isn't sick.
Assuming your dad's health isn't the problem
and the room temperature is nice and warm (around 68 degrees Fahrenheit), it may be that he's staying in the shower or tub too long. Try shorter baths.
Always make sure the water is warm, checking it with your hand or a bath thermometer first. It shouldn't be too warm, though -- not above 90 to 100 degrees F. (Don't leave this up to your dad. He may not be able to gauge temperature well or read the thermometer.)
Keep as much of your father's body covered as you can during a bath, using thick dry towels or even a bathrobe you can clean under. Cover and dry him quickly when you're done.
If your father keeps shivering, he's not only uncomfortable but also at risk for getting a cold or the flu. His body is working so hard trying to stay warm that it leaves fewer immune system resources for fighting illness.
If your dad can't keep warm during a tub bath, you may need to try a different bathing option. He may stay warmer with a quick bed bath because his whole body won't have to get wet at once.
Many people think anything short of a shower or bath won't result in a thorough washing, but I disagree. You can keep your dad clean without soaking him head to toe. Focus on cleaning his face, underarms, and private areas daily. If you work on a small area each day, you can eventually clean the entire body.