You can use a HELOC to buy another house. Never done it myself, but I've seen it mentioned on threads before.
Do the paperwork on the HELOC. They're often useful to have around anyways. Once you know the credit limit and the rate, make your decision then about how much $ to invest.
Alternatively, pick a conservative investment like a bond fund that gets you something better than 0%.
I used a HELOC to pay off the original high-interest mortgage on our first house. Cut interest by ~3.5% Sure, the HELOC was adjustable, eventually. But it would have been almost impossible to not come out ahead with the restrictions on adjusting. Why a HELOC? No closing costs. The remaining loan was small enough that the closing costs were just disproportionate.
I used a moderately complex strategy to buy the second house when we moved.
When we were planning to buy another house, we went interest-only on our HELOC payments to get us over 10% for the down payment on the new house.
80% conventional first mortgage (fixed)
10% second mortgage (fixed)
10% down payment
When the first house was sold, paid off the HELOC and the second mortgage with a fair amount of cash left over.
NOTE: The first house was in a college town in an area that was mostly rentals. We knew sales were good in the area, and we could easily rent it if it didn't sell - but didn't want to be absentee landlords for college students. Probably should have hired a management company - but that's hindsight.