My dryer heating element broke in two: Can I just wrap the ends together?
Sorry to be the Nay Sayer here, but trying to repair a 240VAC heating coil element is just plain dangerous. You mentioned using aluminum wire, WRONG! That wire will melt in a heartbeat as soon as you turn it on. The heating element is probably made of tungsten or other hardened heat producing metals and trying to use copper or aluminum is no substitute.

Don't risk burning up other parts of your dryer or even your entire house. Order the correct part or go pick one up at a local appliance repair shop and do the job properly and safely.