Service Question

Hello Everyone,
I am new to Fchat and would appreciate any comments or guidance for the following issue. I have a 2002 360 spyder that I got from BJ auction in 2019. It came with full service records with a fluid and belt service done soon before I got it. I used the car sparingly on nice days and a few car shows. It has 7600 miles now and I probably put about 400 miles on it over the last few years. It always ran great without any mechanical or over heating issues. I start it up about once a month during the winter months. My plan was to have the timing belt and new fluids done this spring figuring I am overdue since it has been 4 years. So yesterday it started it up in my garage to let it run for 10-15 minutes. After 10 minutes I went back and saw coolant puddle under the car. It started from the front and inside of the drivers rear tire. I would say about 1/4-1/2 gallon of coolant was on the floor. My garage is pitched so the coolant was going toward the garage door. I immediately shut off the car and opened engine hood. The temp gauge was high but just before the needle hit the red marking on the gauge. Car seemed to cool down fast. I opened the coolant cap and didn't see much fluid in there. I saw a little green fluid on top of the aluminum where the coolant tank attaches too and I didn't see any along the drivers side of engine looking from the top. Garage never gets below 40 degrees.
I live in Westchester County, NY
1. What would cause that all of a sudden?
2. There were previous service records from Miller in Greenwich but I wanted other service options in the area.
Any recommendations would be much appreciate. I need a fluid service and belt service and to fix the coolant problem. I would like for the car to get picked up and brought back. My choices for dealers near me are Miller and WWOF. Are there any good private shops that can handle that car and do pick up and return?

Thanks Adam

 

Thanks for responding. There was no oil in the coolant so hopefully its not a bad heat exchanger

 

It may be related to fans, I was looking thru a old service record and the fan relays needed to be replaced 5 years ago.