1. A method of cooling a gas turbine engine [10] having a compressor [24, 26] with multiple, axially arranged stages [52, 54] of paired rotating blades [56, 58] and stationary vanes [60, 62] located between an outer compressor casing [82] and inner compressor casing [80], the method comprising a closed loop cooling of the compressor [24, 26] by routing a liquid coolant [98, 100] through the vanes [60, 62] of at least some of the stages [52, 54] and through an intercooler [88] to draw heat into the liquid coolant [98, 100] and routing the heated liquid coolant [98, 100] through a heat exchanger [76].
2. The method as claimed in claim 1 wherein the routing the liquid coolant [98, 100] through at least some of the vanes [60, 62] comprises routing the liquid coolant [98, 100] through variable stator vanes [60, 62].
3. The method as claimed in claim 2 wherein the routing the liquid coolant [98, 100] through at least some of the vanes [60, 62] comprises routing the liquid coolant [98, 100] through non-variable stator vanes [60, 62].
4. The method as claimed in claim 1 wherein the routing the liquid coolant [98, 100] through the intercooler [88] comprises routing the liquid coolant [98, 100] through a heat exchanger [76].
5. The method as claimed in claim 4 wherein the routing the liquid coolant [98, 100] through the heat exchanger [76] comprises routing the liquid coolant [98, 100] through a heat exchanger [76] located upstream of the compressor [24, 26].
6. The method as claimed in claim 4 wherein the routing the liquid coolant [98, 100] through a heat exchanger [76] comprises routing the liquid coolant [98, 100] through at least one of inlet guide vanes [55] and outlet guide vanes [57] for the compressor [24, 26].
7. The method as claimed in claim 1 further comprising passing a cooling fluid [75] through the heat exchanger [76].

8. The method as claimed in claim 6 wherein the cooling fluid [75]
comprises air from a fan section [18] of the gas turbine engine [10].