Is there a way to join copper and aluminium?

How to mix solid aluminium sheet with solid copper sheet (using heat?) to make a compound.

I'm not sure if I correctly understand your question - that is, whether you're asking how to physically fasten copper and aluminum pieces together, or of you're asking how to make intermetallic compounds of copper and aluminum. Since you did mention a compound, though, I'm guessing the latter. Copper and aluminum do react to form a number of intermetallic compounds. Among these are Al4Cu9, AlCu, and Al2Cu (see first reference below). These are referred to as aluminides of copper, and may be prepared by melting the two metals together in the proper ratio by weight and cooling slowly. For example, Al2Cu (also called CuAl2) may be prepared by melting a mixture containing 96% aluminum and 4% copper (see second reference below). Note that a protective inert atmosphere is desirable for any work of this sort to prevent oxidation. CORRECTION: The compound CuAl2 contains about 54% copper and 46% aluminum (NOT as above). It's the 2000 series aluminum alloys which contain around 4% copper, and it is the precipitation of CuAl2 during heat treatment which makes them hardenable. The final sentence in the second paragraph above should read: For example, Al2Cu (also called CuAl2) may be prepared by melting a mixture containing 46% aluminum and 54% copper (see second reference below).

Aluminium and copper can be used to produce an alloy (see the first link, under wrought alloys). The alloy strength is comparable to steel. Aluminium melts at around 660C and copper at 1084C, so you'd need special burners to produce that kind of heat. An oxyacetylene torch would do it, but more readily available gases like propane and butane mixed with air would also suffice.

As copper and aluminum are both metals and both have positive charges, you can not form a compound with them. You can, however, create an alloy out of them.

I don't think you can make them into a compound, but by heating them to a certain temperature, I believe you can turn them into an alloy, or solution of metals.