The problem is that marketing calls USB-C card thunderbolt when it doesn't actually support it.  There is no standard for a PCI-E card that has thunderbolt. Each vendor makes their own card and cables and and and and. If your board doesn't have a Thunderbolt 3 controller and header you cant add this later. Thunderbolt™ 3 PCIe Card as optional standard specs. EDIT

https://www.delltechnologies.com/en-us/collaterals/unauth/data-sheets/products/workstations/1053-3640-tower-spec-sheet-final.pdf

If thunderbolt security is greyed out or doesn't exist at all in your bios then there is nothing you can buy that will add this feature.

Thunderbolt 3 header and controller on motherboard ARE REQUIRED.

Any add on card also needs a 5 pin GPIO cable to go from the card to the motherboard controller AND an additional Display port wrap thru cable for the outside. In general if you did not order it you cant add it later.

This is how ASUS does it note 2 cables one internal and one external This is the case for thunderbolt 2 or 3

Systems with USB Type-C Port Lack a Thunderbolt 3 Controller

 If the system was not ordered with the Thunderbolt 3 options, it cannot be added at a later time. You should check bios for thunderbolt 3 security.

Systems that have optional Thunderbolt 3 capability will have a USB/Thunderbolt configuration option listed in the BIOS regardless of having a Thunderbolt 3 option installed.

If the system DOES NOT have Thunderbolt 3 capability, the thunderbolt options will be grayed out and cannot be selected in the BIOS. (See picture below)

 No Thunderbolt 3 Capability displayed in BIOS game over.

NO THUNDERBOLT CONTROLLER

I've read the service manual of my Dell Precision 3640 tower several times. There is a contradiction I can't figure out: mentioned is a thunderbolt 3 to pcie (slot 3) add in card. But there is neither a thunderbolt 3 controller (head) on the motherboard nor is Thunderbolt listed in the BIOS. Did I  misinterpret the chapter of the service manual? Thanks for clarification.

I have given up on this as I found a better workaround to what I needed at the time and then moved to a more powerful workstation. 

What I understood is that the TB3 header will be physically present on machines that were pre-configured with the TB3 add-in card, otherwise you will not have the controller and header connector on your motherboard. It cannot be retrofitted.

@anamnesis57 

@his_dudeness 

Thunderbolt Controller on motherboard is OPTIONAL and Cannot be added later.

Intel has abandoned thunderbolt and royalties for hardware and software. Its now public domain software rights via usb sig. Future models will be USB 4.0 with backwards compatability to Thunderbolt 3.

Please press the blue Accept as Solution button below if post answers the question.

Thunderbolt options in BIOS will be greyed out if your board DOES NOT have a controller.

Systems with USB Type-C Port Lack a Thunderbolt 3 Controller

 If the system was not ordered with the Thunderbolt 3 options, it cannot be added at a later time. You should check bios for thunderbolt 3 security.

Systems that have optional Thunderbolt 3 capability will have a USB/Thunderbolt configuration option listed in the BIOS regardless of having a Thunderbolt 3 option installed.

If the system DOES NOT have Thunderbolt 3 capability, the thunderbolt options will be grayed out and cannot be selected in the BIOS. (See picture below)

 No Thunderbolt 3 Capability displayed in BIOS game over.

NO THUNDERBOLT CONTROLLER

Thanks, Speedstep! It's clear now for me. A little footnote in the service manual would be helpful. 

@anamnesis57 

Please Press the blue Accept as Solution button below the posts that answer your questions.

Does the Dell Thunderbolt 3 card work in the Precision T7910? there us support for thunderbolt in the BIOS and looking to get the TB 2 card 07HMHP but the TB 3 would be a better choice? but not paying $500 for one

Dell 555-BEOX / 7XY5K Thunderbolt 3 PCIe Card 2 Type C Ports 1 DP in | eBay

PCIE Thunderbolt 3 Card (Full Height) | Dell USA

@speedstep​ I have Thunderbolt support in BIOS on my Precision T7910 so would TB 3 work or only supports TB 2?

Looks like the only model Dells to support the TB 3 cards are

PART 7XY5K IS UTILISED IN THE FOLLOWING MODELS:

Dell Alienware Aurora R8

Dell Precision R3930, R3930 XL, T3630 XL

speedstep had not posting or replying for quite a year now.  But, for thunderbolt subjects, all his posts were telling people that add-in thunderbolt cards wouldn't work.  Even in contradiction to Dell mods and users whom were successfully reported their working upgrades. 

All I can tell you is the T7910 was designed to use thunderbolt 2 add-in cards.  It will require the header to complete wirings connection.  While thunderbolt 3 compatible systems do not require GPIO header on the motherboards.  Both are still required support in BIOS and bus numbers allocation on designated PCIe slot.