Does anyone know a cheap way to keep cool at night?

Try the "Laurence" method. In the event in which you would like to cool yourself off, you may wish to take your blanket off as this will cool you down or make you "Laurence". If you require some form of cover for protection, maybe you should consider getting a very thin sheet as opposed to a heavy blanket, quilt, or doona.
Plug in your fan and turn it towards you. Purchase a commercial bag of ice cubes. Empty the entire bag into a wide, shallow container (to contain the water as the ice melts) such as a roasting pan. Place the container of ice right in front of the fan (between the fan and you), at the level of the top of the bed. The ice-cooled air will be noticeably cooler than the room air for the amount of time it takes for the ice to melt -- which is as long as it should take for you to fall asleep.
Try the window method. Open your window at night time to let cool air breeze through your house.
Try the towel method. Hang a wet towel from two chairs to hold the ice. The melting ice will wet and chill the towel and the fan will blow that cold air on you. Place a container under the towel to catch the melting ice water. You can use a thread to connect the bottom of the towel with the container to avoid the annoying dripping sound.
 
A cool shower will do wondersTake a cool shower, bath, or wipe your body down with a cool wash cloth. Without fully drying yourself, hop into bed, and let the air slowly dry you. This will keep you cool for a long time, allowing you to fall asleep. If a shower or bath is not an option, splash cool water on your head, and soak your hands and feet in cool water if possible. Your head, hands and feet are your "radiators" and you'll feel cooler faster by focusing on those areas Consider using the "Egyptian Method": wet a sheet or bath towel that is large enough to cover you with cool or cold water, and wring it or run it through the spin cycle on a washing machine until the sheet is quite damp but not dripping wet. Place the dry towel or sheet on your bed underneath your body and use the wet sheet as your blanket. The damp blanket will keep you cool. Or, during an extreme heat wave, take a light t-shirt, wet it, wring it out and wear it. Evaporation from the shirt will help to keep you cool enough to sleep for a few hours. This is a very simple and environment friendly method of staying cool.
Take a pair of cotton socks, rinse them in cold water, wring them until they are damp and put them on. Cooling your feet lowers the overall temperature of your skin and body.