Will this video card destroy my cpu?

No video card will ever destroy your cpu! It might be that your cpu load rises in some games, but that will only make the fan spin faster. If it gets to loud you can buy an after market cooler later.

Okay. I was told that it will most likely cause it to bottleneck, and result in working to hard/overheating

A "bottleneck" means that one component is slower than another and therefore the faster component can only go as fast as the slower one.

Which means in your case: If your CPU can't handle the maximum performance of your 7870, the 7870 will slow down (or in other words never run at it's full potential).

And that's about it.

If for whatever reason your CPU cooler can't keep up with the CPU running at 100% for a long time. Just get a cheap aftermarket cooler like the CoolerMaster 212+ and temperature shouldn't be an issue.

Thats what i was planning on in the future. Im currently buying upgrades for this pc that i will later build into a whole new system

PCPartPicker part list: http://pcpartpicker.com/p/hmTH
Price breakdown by merchant: http://pcpartpicker.com/p/hmTH/by_merchant/
Benchmarks: http://pcpartpicker.com/p/hmTH/benchmarks/

CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($215.98 @ NCIX US)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($27.98 @ NCIX US)
Motherboard: ASRock Z77 Extreme4 ATX LGA1155 Motherboard ($134.99 @ Amazon)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($41.10 @ NCIX US)
Video Card: HIS Radeon HD 7870 2GB Video Card ($199.99 @ Newegg)
Case: Cooler Master HAF 912 ATX Mid Tower Case ($49.49 @ SuperBiiz)
Power Supply: PC Power & Cooling Silencer MK III 600W 80 PLUS Bronze Certified ATX12V Power Supply ($69.33 @ NCIX US)
Operating System: Microsoft Windows 7 Home Premium SP1 (64-bit) ($90.59 @ Amazon)
Total: $829.45
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2012-09-16 16:22 EDT-0400)