I agree about the bypass + remap = win win and less cost
77C is well low - i now see 90C within 10-12 mins a cold (morning)start. I think 1 or both of your stats are not working properly. It's a very common issue for the E60. If your handy with a spanner then swap the EGR stat yourself as i'm told it's easy to get to, and then check again.
If your like me, and not very good with mechanicals, get a knowledgeable Indy to swap both for £300 - £400 inc parts/coolant.
remember if the gr stat doesn't fix it - you will have to replace the coolant for a 2nd time!
once done - you will notice better consumption and a more responsive car